TPTP Problem File: SWW474^3.p

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%------------------------------------------------------------------------------
% File     : SWW474^3 : TPTP v7.2.0. Released v5.3.0.
% Domain   : Software Verification
% Problem  : Hoare's Logic with Procedures line 440, 1000 axioms selected
% Version  : Especial.
% English  :

% Refs     : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
%          : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% Source   : [Bla11]
% Names    : hoare_1000_thf_l440 [Bla11]

% Status   : Theorem
% Rating   : 0.67 v7.2.0, 0.62 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.71 v5.5.0, 0.67 v5.4.0, 1.00 v5.3.0
% Syntax   : Number of formulae    : 1408 (   2 unit; 183 type;   0 defn)
%            Number of atoms       : 13590 ( 988 equality;7664 variable)
%            Maximal formula depth :   19 (   8 average)
%            Number of connectives : 10746 ( 357   ~;  44   |; 164   &;8598   @)
%                                         ( 250 <=>;1333  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of type conns  : 3712 (3712   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  191 ( 183   :;   0   =)
%            Number of variables   : 3382 (  23 sgn;3110   !;  78   ?; 194   ^)
%                                         (3382   :;   0  !>;   0  ?*)
%                                         (   0  @-;   0  @+)
% SPC      : TH0_THM_EQU_NAR

% Comments : This file was generated by Isabelle (most likely Sledgehammer)
%            2011-08-09 20:06:01
%------------------------------------------------------------------------------
%----Should-be-implicit typings (7)
thf(ty_ty_tc__Com__Ocom,type,(
    com: $tType )).

thf(ty_ty_tc__Com__Opname,type,(
    pname: $tType )).

thf(ty_ty_tc__Com__Ostate,type,(
    state: $tType )).

thf(ty_ty_tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,(
    hoare_1708887482_state: $tType )).

thf(ty_ty_tc__Option__Ooption_Itc__Com__Ocom_J,type,(
    option_com: $tType )).

thf(ty_ty_tc__Option__Ooption_Itc__Com__Opname_J,type,(
    option_pname: $tType )).

thf(ty_ty_tc__Option__Ooption_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Co,type,(
    option1624383643_state: $tType )).

%----Explicit typings (176)
thf(sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Com__Opname_M_Eo_J,type,(
    big_la1126801287name_o: ( ( pname > $o ) > $o ) > pname > $o )).

thf(sy_c_Big__Operators_Olattice__class_OInf__fin_000_062_Itc__Hoare____Mirabelle___,type,(
    big_la781588935tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Com_OWT,type,(
    wt: com > $o )).

thf(sy_c_Com_OWT__bodies,type,(
    wT_bodies: $o )).

thf(sy_c_Com_Obody,type,(
    body: pname > option_com )).

thf(sy_c_Com_Ocom_OBODY,type,(
    body_1: pname > com )).

thf(sy_c_Com_Ocom_OSKIP,type,(
    skip: com )).

thf(sy_c_Com_Ocom_OSemi,type,(
    semi: com > com > com )).

thf(sy_c_Com_Ocom_OWhile,type,(
    while: ( state > $o ) > com > com )).

thf(sy_c_Finite__Set_Ocomp__fun__idem_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__C,type,(
    finite138924780name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > $o )).

thf(sy_c_Finite__Set_Ocomp__fun__idem_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv_,type,(
    finite2034616076tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Finite__Set_Ocomp__fun__idem_000_Eo_000_Eo,type,(
    finite2048025996em_o_o: ( $o > $o > $o ) > $o )).

thf(sy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Ocom_000_062_Itc__Com__Ocom_M_Eo_J,type,(
    finite567462577_com_o: ( com > ( com > $o ) > com > $o ) > $o )).

thf(sy_c_Finite__Set_Ocomp__fun__idem_000tc__Com__Opname_000_062_Itc__Com__Opname_M_,type,(
    finite1123817265name_o: ( pname > ( pname > $o ) > pname > $o ) > $o )).

thf(sy_c_Finite__Set_Ocomp__fun__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otrip,type,(
    finite662762081tate_o: ( hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,(
    finite1066544169me_o_o: ( ( ( pname > $o ) > $o ) > $o ) > $o )).

thf(sy_c_Finite__Set_Ofinite_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,(
    finite1019950101te_o_o: ( ( ( hoare_1708887482_state > $o ) > $o ) > $o ) > $o )).

thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Com__Opname_M_Eo_J,type,(
    finite297249702name_o: ( ( pname > $o ) > $o ) > $o )).

thf(sy_c_Finite__Set_Ofinite_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_,type,(
    finite1329924456tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > $o )).

thf(sy_c_Finite__Set_Ofinite_000_Eo,type,(
    finite_finite_o: ( $o > $o ) > $o )).

thf(sy_c_Finite__Set_Ofinite_000tc__Com__Ocom,type,(
    finite_finite_com: ( com > $o ) > $o )).

thf(sy_c_Finite__Set_Ofinite_000tc__Com__Opname,type,(
    finite_finite_pname: ( pname > $o ) > $o )).

thf(sy_c_Finite__Set_Ofinite_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__C,type,(
    finite1625599783_state: ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Finite__Set_Ofold_000_062_Itc__Com__Opname_M_Eo_J_000_062_I_062_Itc__Com__O,type,(
    finite1849951719me_o_o: ( ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).

thf(sy_c_Finite__Set_Ofold_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_,type,(
    finite472615016name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( pname > $o ) > ( ( pname > $o ) > $o ) > pname > $o )).

thf(sy_c_Finite__Set_Ofold_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,type,(
    finite463603445te_o_o: ( ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Finite__Set_Ofold_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It_001,type,(
    finite822533768tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Finite__Set_Ofold_000_Eo_000_Eo,type,(
    finite_fold_o_o: ( $o > $o > $o ) > $o > ( $o > $o ) > $o )).

thf(sy_c_Finite__Set_Ofold_000tc__Com__Ocom_000_062_Itc__Com__Ocom_M_Eo_J,type,(
    finite504235573_com_o: ( com > ( com > $o ) > com > $o ) > ( com > $o ) > ( com > $o ) > com > $o )).

thf(sy_c_Finite__Set_Ofold_000tc__Com__Ocom_000tc__Com__Ocom,type,(
    finite_fold_com_com: ( com > com > com ) > com > ( com > $o ) > com )).

thf(sy_c_Finite__Set_Ofold_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,(
    finite603803317name_o: ( pname > ( pname > $o ) > pname > $o ) > ( pname > $o ) > ( pname > $o ) > pname > $o )).

thf(sy_c_Finite__Set_Ofold_000tc__Com__Opname_000tc__Com__Opname,type,(
    finite1657623752_pname: ( pname > pname > pname ) > pname > ( pname > $o ) > pname )).

thf(sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,type,(
    finite96880613tate_o: ( hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Finite__Set_Ofold_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com_002,type,(
    finite309095018_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state )).

thf(sy_c_Finite__Set_Ofold__image_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otr,type,(
    finite2139561282_pname: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( pname > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( pname > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Com__Opname_M_Eo_J,type,(
    finite349908348name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o )).

thf(sy_c_Finite__Set_Ofolding__one_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,(
    finite928843026tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Ocom,type,(
    finite860057415ne_com: ( com > com > com ) > ( ( com > $o ) > com ) > $o )).

thf(sy_c_Finite__Set_Ofolding__one_000tc__Com__Opname,type,(
    finite1282449217_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o )).

thf(sy_c_Finite__Set_Ofolding__one_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_,type,(
    finite1615457021_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o )).

thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Com__Opname_M_Eo_J,type,(
    finite697516351name_o: ( ( pname > $o ) > ( pname > $o ) > pname > $o ) > ( ( ( pname > $o ) > $o ) > pname > $o ) > $o )).

thf(sy_c_Finite__Set_Ofolding__one__idem_000_062_Itc__Hoare____Mirabelle____nqhfsdfv,type,(
    finite621643279tate_o: ( ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Ocom,type,(
    finite666746948em_com: ( com > com > com ) > ( ( com > $o ) > com ) > $o )).

thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Com__Opname,type,(
    finite89670078_pname: ( pname > pname > pname ) > ( ( pname > $o ) > pname ) > $o )).

thf(sy_c_Finite__Set_Ofolding__one__idem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,(
    finite1347568576_state: ( hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > $o )).

thf(sy_c_Fun_Ofun__upd_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__O,type,(
    fun_up1986763201_state: ( pname > hoare_1708887482_state ) > pname > hoare_1708887482_state > pname > hoare_1708887482_state )).

thf(sy_c_Fun_Ofun__upd_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_J,type,(
    fun_up879233478on_com: ( pname > option_com ) > pname > option_com > pname > option_com )).

thf(sy_c_Fun_Oinj__on_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_M_Eo_,type,(
    inj_on691924881name_o: ( ( pname > $o ) > pname > $o ) > ( ( pname > $o ) > $o ) > $o )).

thf(sy_c_Fun_Oinj__on_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Co,type,(
    inj_on176908593tate_o: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o )).

thf(sy_c_Fun_Oinj__on_000tc__Com__Ocom_000tc__Option__Ooption_Itc__Com__Ocom_J,type,(
    inj_on11367768on_com: ( com > option_com ) > ( com > $o ) > $o )).

thf(sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Com__Opname,type,(
    inj_on_pname_pname: ( pname > pname ) > ( pname > $o ) > $o )).

thf(sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Ot,type,(
    inj_on1553129421_state: ( pname > hoare_1708887482_state ) > ( pname > $o ) > $o )).

thf(sy_c_Fun_Oinj__on_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Opname_J,type,(
    inj_on737724108_pname: ( pname > option_pname ) > ( pname > $o ) > $o )).

thf(sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost,type,(
    inj_on1945914667_pname: ( hoare_1708887482_state > pname ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost_003,type,(
    inj_on632008595_state: ( hoare_1708887482_state > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Fun_Oinj__on_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost_004,type,(
    inj_on945311362_state: ( hoare_1708887482_state > option1624383643_state ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Fun_Ooverride__on_000tc__Com__Opname_000tc__Option__Ooption_Itc__Com__Ocom_,type,(
    overri1496249029on_com: ( pname > option_com ) > ( pname > option_com ) > ( pname > $o ) > pname > option_com )).

thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,(
    minus_1480864103me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).

thf(sy_c_Groups_Ominus__class_Ominus_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsd,type,(
    minus_548038231te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Ocom_M_Eo_J,type,(
    minus_minus_com_o: ( com > $o ) > ( com > $o ) > com > $o )).

thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Com__Opname_M_Eo_J,type,(
    minus_minus_pname_o: ( pname > $o ) > ( pname > $o ) > pname > $o )).

thf(sy_c_Groups_Ominus__class_Ominus_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__,type,(
    minus_2056855718tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_HOL_OThe_000tc__Com__Ocom,type,(
    the_com_1: ( com > $o ) > com )).

thf(sy_c_HOL_OThe_000tc__Com__Opname,type,(
    the_pname: ( pname > $o ) > pname )).

thf(sy_c_HOL_OThe_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_,type,(
    the_Ho851197897_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state )).

thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_OMGT,type,(
    hoare_Mirabelle_MGT: com > hoare_1708887482_state )).

thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__derivs_000tc__Com__Ostate,type,(
    hoare_90032982_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ohoare__valids_000tc__Com__Ostate,type,(
    hoare_496444244_state: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Ostate__not__singleton,type,(
    hoare_1160767572gleton: $o )).

thf(sy_c_Hoare__Mirabelle__nqhfsdfvyv_Otriple_Otriple_000tc__Com__Ostate,type,(
    hoare_858012674_state: ( state > state > $o ) > com > ( state > state > $o ) > hoare_1708887482_state )).

thf(sy_c_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,(
    if_Hoa1374726218_state: $o > hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state )).

thf(sy_c_If_000tc__Option__Ooption_Itc__Com__Ocom_J,type,(
    if_option_com: $o > option_com > option_com > option_com )).

thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Com__Opname_M_Eo_,type,(
    semila2013987940me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).

thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_I_062_Itc__Hoare____Mirabell,type,(
    semila598060698te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Ocom_M_Eo_J,type,(
    semila513601829_com_o: ( com > $o ) > ( com > $o ) > com > $o )).

thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Com__Opname_M_Eo_J,type,(
    semila1673364395name_o: ( pname > $o ) > ( pname > $o ) > pname > $o )).

thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_062_Itc__Hoare____Mirabelle____n,type,(
    semila129691299tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Lattices_Osemilattice__inf__class_Oinf_000_Eo,type,(
    semila854092349_inf_o: $o > $o > $o )).

thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Com__Opname_M_Eo_,type,(
    semila181081674me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).

thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_I_062_Itc__Hoare____Mirabell,type,(
    semila1853742644te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Ocom_M_Eo_J,type,(
    semila1562558655_com_o: ( com > $o ) > ( com > $o ) > com > $o )).

thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Com__Opname_M_Eo_J,type,(
    semila1780557381name_o: ( pname > $o ) > ( pname > $o ) > pname > $o )).

thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_062_Itc__Hoare____Mirabelle____n,type,(
    semila1122118281tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Lattices_Osemilattice__sup__class_Osup_000_Eo,type,(
    semila10642723_sup_o: $o > $o > $o )).

thf(sy_c_Map_Odom_000tc__Com__Ocom_000tc__Com__Ocom,type,(
    dom_com_com: ( com > option_com ) > com > $o )).

thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom,type,(
    dom_pname_com: ( pname > option_com ) > pname > $o )).

thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Opname,type,(
    dom_pname_pname: ( pname > option_pname ) > pname > $o )).

thf(sy_c_Map_Odom_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otripl,type,(
    dom_pn1412407212_state: ( pname > option1624383643_state ) > pname > $o )).

thf(sy_c_Map_Odom_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_,type,(
    dom_Ho1805192458_pname: ( hoare_1708887482_state > option_pname ) > hoare_1708887482_state > $o )).

thf(sy_c_Map_Odom_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate__005,type,(
    dom_Ho1703271284_state: ( hoare_1708887482_state > option1624383643_state ) > hoare_1708887482_state > $o )).

thf(sy_c_Map_Orestrict__map_000tc__Com__Opname_000tc__Com__Ocom,type,(
    restri1382200118me_com: ( pname > option_com ) > ( pname > $o ) > pname > option_com )).

thf(sy_c_Natural_Oevalc,type,(
    evalc: com > state > state > $o )).

thf(sy_c_Option_Ois__none_000tc__Com__Ocom,type,(
    is_none_com: option_com > $o )).

thf(sy_c_Option_Ois__none_000tc__Com__Opname,type,(
    is_none_pname: option_pname > $o )).

thf(sy_c_Option_Ois__none_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com_,type,(
    is_non163157940_state: option1624383643_state > $o )).

thf(sy_c_Option_Ooption_ONone_000tc__Com__Ocom,type,(
    none_com: option_com )).

thf(sy_c_Option_Ooption_ONone_000tc__Com__Opname,type,(
    none_pname: option_pname )).

thf(sy_c_Option_Ooption_ONone_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__,type,(
    none_H1106584047_state: option1624383643_state )).

thf(sy_c_Option_Ooption_OSome_000tc__Com__Ocom,type,(
    some_com: com > option_com )).

thf(sy_c_Option_Ooption_OSome_000tc__Com__Opname,type,(
    some_pname: pname > option_pname )).

thf(sy_c_Option_Ooption_OSome_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__,type,(
    some_H1974565227_state: hoare_1708887482_state > option1624383643_state )).

thf(sy_c_Option_Oset_000tc__Com__Ocom,type,(
    set_com: option_com > com > $o )).

thf(sy_c_Option_Oset_000tc__Com__Opname,type,(
    set_pname: option_pname > pname > $o )).

thf(sy_c_Option_Oset_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Osta,type,(
    set_Ho525251890_state: option1624383643_state > hoare_1708887482_state > $o )).

thf(sy_c_Option_Othe_000tc__Com__Ocom,type,(
    the_com: option_com > com )).

thf(sy_c_Option_Othe_000tc__Com__Opname,type,(
    the_pname_1: option_pname > pname )).

thf(sy_c_Option_Othe_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Osta,type,(
    the_Ho963921505_state: option1624383643_state > hoare_1708887482_state )).

thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,(
    bot_bot_pname_o_o: ( pname > $o ) > $o )).

thf(sy_c_Orderings_Obot__class_Obot_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdf,type,(
    bot_bo1678742418te_o_o: ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Ocom_M_Eo_J,type,(
    bot_bot_com_o: com > $o )).

thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Com__Opname_M_Eo_J,type,(
    bot_bot_pname_o: pname > $o )).

thf(sy_c_Orderings_Obot__class_Obot_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__O,type,(
    bot_bo19817387tate_o: hoare_1708887482_state > $o )).

thf(sy_c_Orderings_Obot__class_Obot_000_Eo,type,(
    bot_bot_o: $o )).

thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_,type,(
    ord_le1205211808me_o_o: ( ( pname > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o )).

thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_I_062_Itc__Hoare____Mirabelle____nq,type,(
    ord_le1728773982te_o_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o )).

thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Ocom_M_Eo_J,type,(
    ord_less_eq_com_o: ( com > $o ) > ( com > $o ) > $o )).

thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Com__Opname_M_Eo_J,type,(
    ord_less_eq_pname_o: ( pname > $o ) > ( pname > $o ) > $o )).

thf(sy_c_Orderings_Oord__class_Oless__eq_000_062_Itc__Hoare____Mirabelle____nqhfsdfv,type,(
    ord_le777019615tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Orderings_Oord__class_Oless__eq_000_Eo,type,(
    ord_less_eq_o: $o > $o > $o )).

thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__Com__Ocom_M_Eo_J,type,(
    top_top_com_o: com > $o )).

thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__Com__Opname_M_Eo_J,type,(
    top_top_pname_o: pname > $o )).

thf(sy_c_Orderings_Otop__class_Otop_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__O,type,(
    top_to832624271tate_o: hoare_1708887482_state > $o )).

thf(sy_c_Partial__Function_Oflat__lub_000tc__Com__Ocom,type,(
    partial_flat_lub_com: com > ( com > $o ) > com )).

thf(sy_c_Partial__Function_Oflat__lub_000tc__Com__Opname,type,(
    partia752020666_pname: pname > ( pname > $o ) > pname )).

thf(sy_c_Partial__Function_Oflat__lub_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otrip,type,(
    partia1256728516_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state )).

thf(sy_c_Set_OCollect_000_062_I_062_Itc__Com__Opname_M_Eo_J_M_Eo_J,type,(
    collect_pname_o_o: ( ( ( pname > $o ) > $o ) > $o ) > ( ( pname > $o ) > $o ) > $o )).

thf(sy_c_Set_OCollect_000_062_I_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_I,type,(
    collec58007891te_o_o: ( ( ( hoare_1708887482_state > $o ) > $o ) > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o )).

thf(sy_c_Set_OCollect_000_062_Itc__Com__Opname_M_Eo_J,type,(
    collect_pname_o: ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).

thf(sy_c_Set_OCollect_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Co,type,(
    collec219771562tate_o: ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Set_OCollect_000tc__Com__Ocom,type,(
    collect_com: ( com > $o ) > com > $o )).

thf(sy_c_Set_OCollect_000tc__Com__Opname,type,(
    collect_pname: ( pname > $o ) > pname > $o )).

thf(sy_c_Set_OCollect_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost,type,(
    collec1568722789_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000_062_Itc__Com__Opname_M_Eo_J,type,(
    image_1085733413name_o: ( ( pname > $o ) > pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).

thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Com__Opname,type,(
    image_pname_o_pname: ( ( pname > $o ) > pname ) > ( ( pname > $o ) > $o ) > pname > $o )).

thf(sy_c_Set_Oimage_000_062_Itc__Com__Opname_M_Eo_J_000tc__Hoare____Mirabelle____nqh,type,(
    image_1922967206_state: ( ( pname > $o ) > hoare_1708887482_state ) > ( ( pname > $o ) > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com_,type,(
    image_909543877tate_o: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__006,type,(
    image_2051418740_pname: ( ( hoare_1708887482_state > $o ) > pname ) > ( ( hoare_1708887482_state > $o ) > $o ) > pname > $o )).

thf(sy_c_Set_Oimage_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__007,type,(
    image_27005066_state: ( ( hoare_1708887482_state > $o ) > hoare_1708887482_state ) > ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Set_Oimage_000tc__Com__Ocom_000tc__Com__Ocom,type,(
    image_com_com: ( com > com ) > ( com > $o ) > com > $o )).

thf(sy_c_Set_Oimage_000tc__Com__Ocom_000tc__Com__Opname,type,(
    image_com_pname: ( com > pname ) > ( com > $o ) > pname > $o )).

thf(sy_c_Set_Oimage_000tc__Com__Ocom_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otripl,type,(
    image_934102463_state: ( com > hoare_1708887482_state ) > ( com > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Com__Opname_M_Eo_J,type,(
    image_pname_pname_o: ( pname > pname > $o ) > ( pname > $o ) > ( pname > $o ) > $o )).

thf(sy_c_Set_Oimage_000tc__Com__Opname_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv,type,(
    image_425134806tate_o: ( pname > hoare_1708887482_state > $o ) > ( pname > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Ocom,type,(
    image_pname_com: ( pname > com ) > ( pname > $o ) > com > $o )).

thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname,type,(
    image_pname_pname: ( pname > pname ) > ( pname > $o ) > pname > $o )).

thf(sy_c_Set_Oimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otri,type,(
    image_1116629049_state: ( pname > hoare_1708887482_state ) > ( pname > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat,type,(
    image_1552895654name_o: ( hoare_1708887482_state > pname > $o ) > ( hoare_1708887482_state > $o ) > ( pname > $o ) > $o )).

thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_008,type,(
    image_1551509096tate_o: ( hoare_1708887482_state > hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_009,type,(
    image_1604448413te_com: ( hoare_1708887482_state > com ) > ( hoare_1708887482_state > $o ) > com > $o )).

thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_010,type,(
    image_1509414295_pname: ( hoare_1708887482_state > pname ) > ( hoare_1708887482_state > $o ) > pname > $o )).

thf(sy_c_Set_Oimage_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostat_011,type,(
    image_757158439_state: ( hoare_1708887482_state > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Set_Oinsert_000_062_Itc__Com__Opname_M_Eo_J,type,(
    insert_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > ( pname > $o ) > $o )).

thf(sy_c_Set_Oinsert_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,type,(
    insert949073679tate_o: ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_Set_Oinsert_000_Eo,type,(
    insert_o: $o > ( $o > $o ) > $o > $o )).

thf(sy_c_Set_Oinsert_000tc__Com__Ocom,type,(
    insert_com: com > ( com > $o ) > com > $o )).

thf(sy_c_Set_Oinsert_000tc__Com__Opname,type,(
    insert_pname: pname > ( pname > $o ) > pname > $o )).

thf(sy_c_Set_Oinsert_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Osta,type,(
    insert528405184_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o )).

thf(sy_c_Set_Othe__elem_000tc__Com__Ocom,type,(
    the_elem_com: ( com > $o ) > com )).

thf(sy_c_Set_Othe__elem_000tc__Com__Opname,type,(
    the_elem_pname: ( pname > $o ) > pname )).

thf(sy_c_Set_Othe__elem_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__O,type,(
    the_el864710747_state: ( hoare_1708887482_state > $o ) > hoare_1708887482_state )).

thf(sy_c_Set_Ovimage_000tc__Com__Opname_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otr,type,(
    vimage1943311875_state: ( pname > hoare_1708887482_state ) > ( hoare_1708887482_state > $o ) > pname > $o )).

thf(sy_c_fequal_000_062_Itc__Com__Opname_M_Eo_J,type,(
    fequal_pname_o: ( pname > $o ) > ( pname > $o ) > $o )).

thf(sy_c_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost,type,(
    fequal1436017556tate_o: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_c_fequal_000tc__Com__Ocom,type,(
    fequal_com: com > com > $o )).

thf(sy_c_fequal_000tc__Com__Opname,type,(
    fequal_pname: pname > pname > $o )).

thf(sy_c_fequal_000tc__Com__Ostate,type,(
    fequal_state: state > state > $o )).

thf(sy_c_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,(
    fequal224822779_state: hoare_1708887482_state > hoare_1708887482_state > $o )).

thf(sy_c_member_000_062_Itc__Com__Opname_M_Eo_J,type,(
    member_pname_o: ( pname > $o ) > ( ( pname > $o ) > $o ) > $o )).

thf(sy_c_member_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ost,type,(
    member814030440tate_o: ( hoare_1708887482_state > $o ) > ( ( hoare_1708887482_state > $o ) > $o ) > $o )).

thf(sy_c_member_000_Eo,type,(
    member_o: $o > ( $o > $o ) > $o )).

thf(sy_c_member_000tc__Com__Ocom,type,(
    member_com: com > ( com > $o ) > $o )).

thf(sy_c_member_000tc__Com__Opname,type,(
    member_pname: pname > ( pname > $o ) > $o )).

thf(sy_c_member_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate_J,type,(
    member451959335_state: hoare_1708887482_state > ( hoare_1708887482_state > $o ) > $o )).

thf(sy_v_Fa,type,(
    fa: hoare_1708887482_state > $o )).

thf(sy_v_pn,type,(
    pn: pname )).

thf(sy_v_y,type,(
    y: com )).

%----Relevant facts (1199)
thf(fact_0_empty,axiom,(
    ! [G_7: hoare_1708887482_state > $o] :
      ( hoare_90032982_state @ G_7 @ bot_bo19817387tate_o ) )).

thf(fact_1_asm,axiom,(
    ! [Ts_7: hoare_1708887482_state > $o,G_39: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ Ts_7 @ G_39 )
     => ( hoare_90032982_state @ G_39 @ Ts_7 ) ) )).

thf(fact_2_weaken,axiom,(
    ! [Ts_6: hoare_1708887482_state > $o,G_38: hoare_1708887482_state > $o,Ts_5: hoare_1708887482_state > $o] :
      ( ( hoare_90032982_state @ G_38 @ Ts_5 )
     => ( ( ord_le777019615tate_o @ Ts_6 @ Ts_5 )
       => ( hoare_90032982_state @ G_38 @ Ts_6 ) ) ) )).

thf(fact_3_thin,axiom,(
    ! [G_37: hoare_1708887482_state > $o,G_36: hoare_1708887482_state > $o,Ts_4: hoare_1708887482_state > $o] :
      ( ( hoare_90032982_state @ G_36 @ Ts_4 )
     => ( ( ord_le777019615tate_o @ G_36 @ G_37 )
       => ( hoare_90032982_state @ G_37 @ Ts_4 ) ) ) )).

thf(fact_4_cut,axiom,(
    ! [G_35: hoare_1708887482_state > $o,G_34: hoare_1708887482_state > $o,Ts_3: hoare_1708887482_state > $o] :
      ( ( hoare_90032982_state @ G_34 @ Ts_3 )
     => ( ( hoare_90032982_state @ G_35 @ G_34 )
       => ( hoare_90032982_state @ G_35 @ Ts_3 ) ) ) )).

thf(fact_5_hoare__derivs_Oinsert,axiom,(
    ! [Ts_2: hoare_1708887482_state > $o,G_33: hoare_1708887482_state > $o,T_3: hoare_1708887482_state] :
      ( ( hoare_90032982_state @ G_33 @ ( insert528405184_state @ T_3 @ bot_bo19817387tate_o ) )
     => ( ( hoare_90032982_state @ G_33 @ Ts_2 )
       => ( hoare_90032982_state @ G_33 @ ( insert528405184_state @ T_3 @ Ts_2 ) ) ) ) )).

thf(fact_6_derivs__insertD,axiom,(
    ! [G_32: hoare_1708887482_state > $o,T_2: hoare_1708887482_state,Ts_1: hoare_1708887482_state > $o] :
      ( ( hoare_90032982_state @ G_32 @ ( insert528405184_state @ T_2 @ Ts_1 ) )
     => ( ( hoare_90032982_state @ G_32 @ ( insert528405184_state @ T_2 @ bot_bo19817387tate_o ) )
        & ( hoare_90032982_state @ G_32 @ Ts_1 ) ) ) )).

thf(fact_7_MGT__BodyN,axiom,(
    ! [Pn_1: pname,G_7: hoare_1708887482_state > $o] :
      ( ( hoare_90032982_state @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ G_7 ) @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn_1 ) ) ) @ bot_bo19817387tate_o ) )
     => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ Pn_1 ) ) @ bot_bo19817387tate_o ) ) ) )).

thf(fact_8_finite__Collect__subsets,axiom,(
    ! [A_274: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_274 )
     => ( finite1066544169me_o_o
        @ ( collect_pname_o_o
          @ ^ [B_84: ( pname > $o ) > $o] :
              ( ord_le1205211808me_o_o @ B_84 @ A_274 ) ) ) ) )).

thf(fact_9_finite__Collect__subsets,axiom,(
    ! [A_274: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_274 )
     => ( finite1019950101te_o_o
        @ ( collec58007891te_o_o
          @ ^ [B_84: ( hoare_1708887482_state > $o ) > $o] :
              ( ord_le1728773982te_o_o @ B_84 @ A_274 ) ) ) ) )).

thf(fact_10_finite__Collect__subsets,axiom,(
    ! [A_274: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_274 )
     => ( finite1329924456tate_o
        @ ( collec219771562tate_o
          @ ^ [B_84: hoare_1708887482_state > $o] :
              ( ord_le777019615tate_o @ B_84 @ A_274 ) ) ) ) )).

thf(fact_11_finite__Collect__subsets,axiom,(
    ! [A_274: pname > $o] :
      ( ( finite_finite_pname @ A_274 )
     => ( finite297249702name_o
        @ ( collect_pname_o
          @ ^ [B_84: pname > $o] :
              ( ord_less_eq_pname_o @ B_84 @ A_274 ) ) ) ) )).

thf(fact_12_finite__imageI,axiom,(
    ! [H_2: hoare_1708887482_state > pname > $o,F_88: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ F_88 )
     => ( finite297249702name_o @ ( image_1552895654name_o @ H_2 @ F_88 ) ) ) )).

thf(fact_13_finite__imageI,axiom,(
    ! [H_2: hoare_1708887482_state > hoare_1708887482_state > $o,F_88: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ F_88 )
     => ( finite1329924456tate_o @ ( image_1551509096tate_o @ H_2 @ F_88 ) ) ) )).

thf(fact_14_finite__imageI,axiom,(
    ! [H_2: pname > pname > $o,F_88: pname > $o] :
      ( ( finite_finite_pname @ F_88 )
     => ( finite297249702name_o @ ( image_pname_pname_o @ H_2 @ F_88 ) ) ) )).

thf(fact_15_finite__imageI,axiom,(
    ! [H_2: pname > hoare_1708887482_state > $o,F_88: pname > $o] :
      ( ( finite_finite_pname @ F_88 )
     => ( finite1329924456tate_o @ ( image_425134806tate_o @ H_2 @ F_88 ) ) ) )).

thf(fact_16_finite__imageI,axiom,(
    ! [H_2: ( pname > $o ) > hoare_1708887482_state,F_88: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ F_88 )
     => ( finite1625599783_state @ ( image_1922967206_state @ H_2 @ F_88 ) ) ) )).

thf(fact_17_finite__imageI,axiom,(
    ! [H_2: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,F_88: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ F_88 )
     => ( finite1625599783_state @ ( image_27005066_state @ H_2 @ F_88 ) ) ) )).

thf(fact_18_finite__imageI,axiom,(
    ! [H_2: ( pname > $o ) > pname,F_88: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ F_88 )
     => ( finite_finite_pname @ ( image_pname_o_pname @ H_2 @ F_88 ) ) ) )).

thf(fact_19_finite__imageI,axiom,(
    ! [H_2: ( hoare_1708887482_state > $o ) > pname,F_88: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ F_88 )
     => ( finite_finite_pname @ ( image_2051418740_pname @ H_2 @ F_88 ) ) ) )).

thf(fact_20_finite__imageI,axiom,(
    ! [H_2: pname > hoare_1708887482_state,F_88: pname > $o] :
      ( ( finite_finite_pname @ F_88 )
     => ( finite1625599783_state @ ( image_1116629049_state @ H_2 @ F_88 ) ) ) )).

thf(fact_21_empty__subsetI,axiom,(
    ! [A_273: pname > $o] :
      ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_273 ) )).

thf(fact_22_empty__subsetI,axiom,(
    ! [A_273: com > $o] :
      ( ord_less_eq_com_o @ bot_bot_com_o @ A_273 ) )).

thf(fact_23_empty__subsetI,axiom,(
    ! [A_273: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ bot_bo19817387tate_o @ A_273 ) )).

thf(fact_24_finite_OinsertI,axiom,(
    ! [A_272: com,A_271: com > $o] :
      ( ( finite_finite_com @ A_271 )
     => ( finite_finite_com @ ( insert_com @ A_272 @ A_271 ) ) ) )).

thf(fact_25_finite_OinsertI,axiom,(
    ! [A_272: pname > $o,A_271: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_271 )
     => ( finite297249702name_o @ ( insert_pname_o @ A_272 @ A_271 ) ) ) )).

thf(fact_26_finite_OinsertI,axiom,(
    ! [A_272: hoare_1708887482_state > $o,A_271: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_271 )
     => ( finite1329924456tate_o @ ( insert949073679tate_o @ A_272 @ A_271 ) ) ) )).

thf(fact_27_finite_OinsertI,axiom,(
    ! [A_272: pname,A_271: pname > $o] :
      ( ( finite_finite_pname @ A_271 )
     => ( finite_finite_pname @ ( insert_pname @ A_272 @ A_271 ) ) ) )).

thf(fact_28_finite_OinsertI,axiom,(
    ! [A_272: hoare_1708887482_state,A_271: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_271 )
     => ( finite1625599783_state @ ( insert528405184_state @ A_272 @ A_271 ) ) ) )).

thf(fact_29_finite_OemptyI,axiom,
    ( finite297249702name_o @ bot_bot_pname_o_o )).

thf(fact_30_finite_OemptyI,axiom,
    ( finite1329924456tate_o @ bot_bo1678742418te_o_o )).

thf(fact_31_finite_OemptyI,axiom,
    ( finite_finite_com @ bot_bot_com_o )).

thf(fact_32_finite_OemptyI,axiom,
    ( finite1625599783_state @ bot_bo19817387tate_o )).

thf(fact_33_finite_OemptyI,axiom,
    ( finite_finite_pname @ bot_bot_pname_o )).

thf(fact_34_finite__Collect__conjI,axiom,(
    ! [Q_26: ( pname > $o ) > $o,P_45: ( pname > $o ) > $o] :
      ( ( ( finite297249702name_o @ ( collect_pname_o @ P_45 ) )
        | ( finite297249702name_o @ ( collect_pname_o @ Q_26 ) ) )
     => ( finite297249702name_o
        @ ( collect_pname_o
          @ ^ [X_3: pname > $o] :
              ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) )).

thf(fact_35_finite__Collect__conjI,axiom,(
    ! [Q_26: ( hoare_1708887482_state > $o ) > $o,P_45: ( hoare_1708887482_state > $o ) > $o] :
      ( ( ( finite1329924456tate_o @ ( collec219771562tate_o @ P_45 ) )
        | ( finite1329924456tate_o @ ( collec219771562tate_o @ Q_26 ) ) )
     => ( finite1329924456tate_o
        @ ( collec219771562tate_o
          @ ^ [X_3: hoare_1708887482_state > $o] :
              ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) )).

thf(fact_36_finite__Collect__conjI,axiom,(
    ! [Q_26: hoare_1708887482_state > $o,P_45: hoare_1708887482_state > $o] :
      ( ( ( finite1625599783_state @ ( collec1568722789_state @ P_45 ) )
        | ( finite1625599783_state @ ( collec1568722789_state @ Q_26 ) ) )
     => ( finite1625599783_state
        @ ( collec1568722789_state
          @ ^ [X_3: hoare_1708887482_state] :
              ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) )).

thf(fact_37_finite__Collect__conjI,axiom,(
    ! [Q_26: pname > $o,P_45: pname > $o] :
      ( ( ( finite_finite_pname @ ( collect_pname @ P_45 ) )
        | ( finite_finite_pname @ ( collect_pname @ Q_26 ) ) )
     => ( finite_finite_pname
        @ ( collect_pname
          @ ^ [X_3: pname] :
              ( (&) @ ( P_45 @ X_3 ) @ ( Q_26 @ X_3 ) ) ) ) ) )).

thf(fact_38_image__constant__conv,axiom,(
    ! [C_68: pname,A_270: hoare_1708887482_state > $o] :
      ( ( ( A_270 = bot_bo19817387tate_o )
       => ( ( image_1509414295_pname
            @ ^ [X_3: hoare_1708887482_state] : C_68
            @ A_270 )
          = bot_bot_pname_o ) )
      & ( ( A_270 != bot_bo19817387tate_o )
       => ( ( image_1509414295_pname
            @ ^ [X_3: hoare_1708887482_state] : C_68
            @ A_270 )
          = ( insert_pname @ C_68 @ bot_bot_pname_o ) ) ) ) )).

thf(fact_39_image__constant__conv,axiom,(
    ! [C_68: com,A_270: hoare_1708887482_state > $o] :
      ( ( ( A_270 = bot_bo19817387tate_o )
       => ( ( image_1604448413te_com
            @ ^ [X_3: hoare_1708887482_state] : C_68
            @ A_270 )
          = bot_bot_com_o ) )
      & ( ( A_270 != bot_bo19817387tate_o )
       => ( ( image_1604448413te_com
            @ ^ [X_3: hoare_1708887482_state] : C_68
            @ A_270 )
          = ( insert_com @ C_68 @ bot_bot_com_o ) ) ) ) )).

thf(fact_40_image__constant__conv,axiom,(
    ! [C_68: hoare_1708887482_state,A_270: com > $o] :
      ( ( ( A_270 = bot_bot_com_o )
       => ( ( image_934102463_state
            @ ^ [X_3: com] : C_68
            @ A_270 )
          = bot_bo19817387tate_o ) )
      & ( ( A_270 != bot_bot_com_o )
       => ( ( image_934102463_state
            @ ^ [X_3: com] : C_68
            @ A_270 )
          = ( insert528405184_state @ C_68 @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_41_image__constant__conv,axiom,(
    ! [C_68: hoare_1708887482_state,A_270: pname > $o] :
      ( ( ( A_270 = bot_bot_pname_o )
       => ( ( image_1116629049_state
            @ ^ [X_3: pname] : C_68
            @ A_270 )
          = bot_bo19817387tate_o ) )
      & ( ( A_270 != bot_bot_pname_o )
       => ( ( image_1116629049_state
            @ ^ [X_3: pname] : C_68
            @ A_270 )
          = ( insert528405184_state @ C_68 @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_42_image__constant,axiom,(
    ! [C_67: pname,X_119: hoare_1708887482_state,A_269: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ X_119 @ A_269 )
     => ( ( image_1509414295_pname
          @ ^ [X_3: hoare_1708887482_state] : C_67
          @ A_269 )
        = ( insert_pname @ C_67 @ bot_bot_pname_o ) ) ) )).

thf(fact_43_image__constant,axiom,(
    ! [C_67: com,X_119: hoare_1708887482_state,A_269: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ X_119 @ A_269 )
     => ( ( image_1604448413te_com
          @ ^ [X_3: hoare_1708887482_state] : C_67
          @ A_269 )
        = ( insert_com @ C_67 @ bot_bot_com_o ) ) ) )).

thf(fact_44_image__constant,axiom,(
    ! [C_67: pname,X_119: pname,A_269: pname > $o] :
      ( ( member_pname @ X_119 @ A_269 )
     => ( ( image_pname_pname
          @ ^ [X_3: pname] : C_67
          @ A_269 )
        = ( insert_pname @ C_67 @ bot_bot_pname_o ) ) ) )).

thf(fact_45_image__constant,axiom,(
    ! [C_67: com,X_119: pname,A_269: pname > $o] :
      ( ( member_pname @ X_119 @ A_269 )
     => ( ( image_pname_com
          @ ^ [X_3: pname] : C_67
          @ A_269 )
        = ( insert_com @ C_67 @ bot_bot_com_o ) ) ) )).

thf(fact_46_image__constant,axiom,(
    ! [C_67: hoare_1708887482_state,X_119: com,A_269: com > $o] :
      ( ( member_com @ X_119 @ A_269 )
     => ( ( image_934102463_state
          @ ^ [X_3: com] : C_67
          @ A_269 )
        = ( insert528405184_state @ C_67 @ bot_bo19817387tate_o ) ) ) )).

thf(fact_47_image__constant,axiom,(
    ! [C_67: hoare_1708887482_state,X_119: pname,A_269: pname > $o] :
      ( ( member_pname @ X_119 @ A_269 )
     => ( ( image_1116629049_state
          @ ^ [X_3: pname] : C_67
          @ A_269 )
        = ( insert528405184_state @ C_67 @ bot_bo19817387tate_o ) ) ) )).

thf(fact_48_insert__dom,axiom,(
    ! [F_87: com > option_com,X_118: com,Y_53: com] :
      ( ( ( F_87 @ X_118 )
        = ( some_com @ Y_53 ) )
     => ( ( insert_com @ X_118 @ ( dom_com_com @ F_87 ) )
        = ( dom_com_com @ F_87 ) ) ) )).

thf(fact_49_insert__dom,axiom,(
    ! [F_87: hoare_1708887482_state > option_pname,X_118: hoare_1708887482_state,Y_53: pname] :
      ( ( ( F_87 @ X_118 )
        = ( some_pname @ Y_53 ) )
     => ( ( insert528405184_state @ X_118 @ ( dom_Ho1805192458_pname @ F_87 ) )
        = ( dom_Ho1805192458_pname @ F_87 ) ) ) )).

thf(fact_50_insert__dom,axiom,(
    ! [F_87: hoare_1708887482_state > option1624383643_state,X_118: hoare_1708887482_state,Y_53: hoare_1708887482_state] :
      ( ( ( F_87 @ X_118 )
        = ( some_H1974565227_state @ Y_53 ) )
     => ( ( insert528405184_state @ X_118 @ ( dom_Ho1703271284_state @ F_87 ) )
        = ( dom_Ho1703271284_state @ F_87 ) ) ) )).

thf(fact_51_insert__dom,axiom,(
    ! [F_87: pname > option_com,X_118: pname,Y_53: com] :
      ( ( ( F_87 @ X_118 )
        = ( some_com @ Y_53 ) )
     => ( ( insert_pname @ X_118 @ ( dom_pname_com @ F_87 ) )
        = ( dom_pname_com @ F_87 ) ) ) )).

thf(fact_52_finite__surj,axiom,(
    ! [B_171: ( pname > $o ) > $o,F_86: hoare_1708887482_state > pname > $o,A_268: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_268 )
     => ( ( ord_le1205211808me_o_o @ B_171 @ ( image_1552895654name_o @ F_86 @ A_268 ) )
       => ( finite297249702name_o @ B_171 ) ) ) )).

thf(fact_53_finite__surj,axiom,(
    ! [B_171: ( hoare_1708887482_state > $o ) > $o,F_86: hoare_1708887482_state > hoare_1708887482_state > $o,A_268: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_268 )
     => ( ( ord_le1728773982te_o_o @ B_171 @ ( image_1551509096tate_o @ F_86 @ A_268 ) )
       => ( finite1329924456tate_o @ B_171 ) ) ) )).

thf(fact_54_finite__surj,axiom,(
    ! [B_171: pname > $o,F_86: hoare_1708887482_state > pname,A_268: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_268 )
     => ( ( ord_less_eq_pname_o @ B_171 @ ( image_1509414295_pname @ F_86 @ A_268 ) )
       => ( finite_finite_pname @ B_171 ) ) ) )).

thf(fact_55_finite__surj,axiom,(
    ! [B_171: ( pname > $o ) > $o,F_86: pname > pname > $o,A_268: pname > $o] :
      ( ( finite_finite_pname @ A_268 )
     => ( ( ord_le1205211808me_o_o @ B_171 @ ( image_pname_pname_o @ F_86 @ A_268 ) )
       => ( finite297249702name_o @ B_171 ) ) ) )).

thf(fact_56_finite__surj,axiom,(
    ! [B_171: ( hoare_1708887482_state > $o ) > $o,F_86: pname > hoare_1708887482_state > $o,A_268: pname > $o] :
      ( ( finite_finite_pname @ A_268 )
     => ( ( ord_le1728773982te_o_o @ B_171 @ ( image_425134806tate_o @ F_86 @ A_268 ) )
       => ( finite1329924456tate_o @ B_171 ) ) ) )).

thf(fact_57_finite__surj,axiom,(
    ! [B_171: pname > $o,F_86: pname > pname,A_268: pname > $o] :
      ( ( finite_finite_pname @ A_268 )
     => ( ( ord_less_eq_pname_o @ B_171 @ ( image_pname_pname @ F_86 @ A_268 ) )
       => ( finite_finite_pname @ B_171 ) ) ) )).

thf(fact_58_finite__surj,axiom,(
    ! [B_171: hoare_1708887482_state > $o,F_86: ( pname > $o ) > hoare_1708887482_state,A_268: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_268 )
     => ( ( ord_le777019615tate_o @ B_171 @ ( image_1922967206_state @ F_86 @ A_268 ) )
       => ( finite1625599783_state @ B_171 ) ) ) )).

thf(fact_59_finite__surj,axiom,(
    ! [B_171: hoare_1708887482_state > $o,F_86: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,A_268: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_268 )
     => ( ( ord_le777019615tate_o @ B_171 @ ( image_27005066_state @ F_86 @ A_268 ) )
       => ( finite1625599783_state @ B_171 ) ) ) )).

thf(fact_60_finite__surj,axiom,(
    ! [B_171: pname > $o,F_86: ( pname > $o ) > pname,A_268: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_268 )
     => ( ( ord_less_eq_pname_o @ B_171 @ ( image_pname_o_pname @ F_86 @ A_268 ) )
       => ( finite_finite_pname @ B_171 ) ) ) )).

thf(fact_61_finite__surj,axiom,(
    ! [B_171: pname > $o,F_86: ( hoare_1708887482_state > $o ) > pname,A_268: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_268 )
     => ( ( ord_less_eq_pname_o @ B_171 @ ( image_2051418740_pname @ F_86 @ A_268 ) )
       => ( finite_finite_pname @ B_171 ) ) ) )).

thf(fact_62_finite__surj,axiom,(
    ! [B_171: hoare_1708887482_state > $o,F_86: pname > hoare_1708887482_state,A_268: pname > $o] :
      ( ( finite_finite_pname @ A_268 )
     => ( ( ord_le777019615tate_o @ B_171 @ ( image_1116629049_state @ F_86 @ A_268 ) )
       => ( finite1625599783_state @ B_171 ) ) ) )).

thf(fact_63_subset__singletonD,axiom,(
    ! [A_267: pname > $o,X_117: pname] :
      ( ( ord_less_eq_pname_o @ A_267 @ ( insert_pname @ X_117 @ bot_bot_pname_o ) )
     => ( ( A_267 = bot_bot_pname_o )
        | ( A_267
          = ( insert_pname @ X_117 @ bot_bot_pname_o ) ) ) ) )).

thf(fact_64_subset__singletonD,axiom,(
    ! [A_267: com > $o,X_117: com] :
      ( ( ord_less_eq_com_o @ A_267 @ ( insert_com @ X_117 @ bot_bot_com_o ) )
     => ( ( A_267 = bot_bot_com_o )
        | ( A_267
          = ( insert_com @ X_117 @ bot_bot_com_o ) ) ) ) )).

thf(fact_65_subset__singletonD,axiom,(
    ! [A_267: hoare_1708887482_state > $o,X_117: hoare_1708887482_state] :
      ( ( ord_le777019615tate_o @ A_267 @ ( insert528405184_state @ X_117 @ bot_bo19817387tate_o ) )
     => ( ( A_267 = bot_bo19817387tate_o )
        | ( A_267
          = ( insert528405184_state @ X_117 @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_66_MGF,axiom,(
    ! [C_34: com] :
      ( hoare_1160767572gleton
     => ( wT_bodies
       => ( ( wt @ C_34 )
         => ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) ) ) ) ) )).

thf(fact_67_emptyE,axiom,(
    ! [A_266: com] :
      ~ ( member_com @ A_266 @ bot_bot_com_o ) )).

thf(fact_68_emptyE,axiom,(
    ! [A_266: hoare_1708887482_state] :
      ~ ( member451959335_state @ A_266 @ bot_bo19817387tate_o ) )).

thf(fact_69_emptyE,axiom,(
    ! [A_266: pname] :
      ~ ( member_pname @ A_266 @ bot_bot_pname_o ) )).

thf(fact_70_insertCI,axiom,(
    ! [B_170: com,A_265: com,B_169: com > $o] :
      ( ( ~ ( member_com @ A_265 @ B_169 )
       => ( A_265 = B_170 ) )
     => ( member_com @ A_265 @ ( insert_com @ B_170 @ B_169 ) ) ) )).

thf(fact_71_insertCI,axiom,(
    ! [B_170: pname,A_265: pname,B_169: pname > $o] :
      ( ( ~ ( member_pname @ A_265 @ B_169 )
       => ( A_265 = B_170 ) )
     => ( member_pname @ A_265 @ ( insert_pname @ B_170 @ B_169 ) ) ) )).

thf(fact_72_insertCI,axiom,(
    ! [B_170: hoare_1708887482_state,A_265: hoare_1708887482_state,B_169: hoare_1708887482_state > $o] :
      ( ( ~ ( member451959335_state @ A_265 @ B_169 )
       => ( A_265 = B_170 ) )
     => ( member451959335_state @ A_265 @ ( insert528405184_state @ B_170 @ B_169 ) ) ) )).

thf(fact_73_insertE,axiom,(
    ! [A_264: com,B_168: com,A_263: com > $o] :
      ( ( member_com @ A_264 @ ( insert_com @ B_168 @ A_263 ) )
     => ( ( A_264 != B_168 )
       => ( member_com @ A_264 @ A_263 ) ) ) )).

thf(fact_74_insertE,axiom,(
    ! [A_264: pname,B_168: pname,A_263: pname > $o] :
      ( ( member_pname @ A_264 @ ( insert_pname @ B_168 @ A_263 ) )
     => ( ( A_264 != B_168 )
       => ( member_pname @ A_264 @ A_263 ) ) ) )).

thf(fact_75_insertE,axiom,(
    ! [A_264: hoare_1708887482_state,B_168: hoare_1708887482_state,A_263: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ A_264 @ ( insert528405184_state @ B_168 @ A_263 ) )
     => ( ( A_264 != B_168 )
       => ( member451959335_state @ A_264 @ A_263 ) ) ) )).

thf(fact_76_equalityI,axiom,(
    ! [A_262: pname > $o,B_167: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_262 @ B_167 )
     => ( ( ord_less_eq_pname_o @ B_167 @ A_262 )
       => ( A_262 = B_167 ) ) ) )).

thf(fact_77_equalityI,axiom,(
    ! [A_262: hoare_1708887482_state > $o,B_167: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_262 @ B_167 )
     => ( ( ord_le777019615tate_o @ B_167 @ A_262 )
       => ( A_262 = B_167 ) ) ) )).

thf(fact_78_subsetD,axiom,(
    ! [C_66: com,A_261: com > $o,B_166: com > $o] :
      ( ( ord_less_eq_com_o @ A_261 @ B_166 )
     => ( ( member_com @ C_66 @ A_261 )
       => ( member_com @ C_66 @ B_166 ) ) ) )).

thf(fact_79_subsetD,axiom,(
    ! [C_66: hoare_1708887482_state,A_261: hoare_1708887482_state > $o,B_166: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_261 @ B_166 )
     => ( ( member451959335_state @ C_66 @ A_261 )
       => ( member451959335_state @ C_66 @ B_166 ) ) ) )).

thf(fact_80_subsetD,axiom,(
    ! [C_66: pname,A_261: pname > $o,B_166: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_261 @ B_166 )
     => ( ( member_pname @ C_66 @ A_261 )
       => ( member_pname @ C_66 @ B_166 ) ) ) )).

thf(fact_81_image__eqI,axiom,(
    ! [A_260: hoare_1708887482_state > $o,B_165: com,F_85: hoare_1708887482_state > com,X_116: hoare_1708887482_state] :
      ( ( B_165
        = ( F_85 @ X_116 ) )
     => ( ( member451959335_state @ X_116 @ A_260 )
       => ( member_com @ B_165 @ ( image_1604448413te_com @ F_85 @ A_260 ) ) ) ) )).

thf(fact_82_image__eqI,axiom,(
    ! [A_260: pname > $o,B_165: com,F_85: pname > com,X_116: pname] :
      ( ( B_165
        = ( F_85 @ X_116 ) )
     => ( ( member_pname @ X_116 @ A_260 )
       => ( member_com @ B_165 @ ( image_pname_com @ F_85 @ A_260 ) ) ) ) )).

thf(fact_83_image__eqI,axiom,(
    ! [A_260: com > $o,B_165: hoare_1708887482_state,F_85: com > hoare_1708887482_state,X_116: com] :
      ( ( B_165
        = ( F_85 @ X_116 ) )
     => ( ( member_com @ X_116 @ A_260 )
       => ( member451959335_state @ B_165 @ ( image_934102463_state @ F_85 @ A_260 ) ) ) ) )).

thf(fact_84_image__eqI,axiom,(
    ! [A_260: com > $o,B_165: pname,F_85: com > pname,X_116: com] :
      ( ( B_165
        = ( F_85 @ X_116 ) )
     => ( ( member_com @ X_116 @ A_260 )
       => ( member_pname @ B_165 @ ( image_com_pname @ F_85 @ A_260 ) ) ) ) )).

thf(fact_85_image__eqI,axiom,(
    ! [A_260: pname > $o,B_165: hoare_1708887482_state,F_85: pname > hoare_1708887482_state,X_116: pname] :
      ( ( B_165
        = ( F_85 @ X_116 ) )
     => ( ( member_pname @ X_116 @ A_260 )
       => ( member451959335_state @ B_165 @ ( image_1116629049_state @ F_85 @ A_260 ) ) ) ) )).

thf(fact_86_equals0D,axiom,(
    ! [A_259: com,A_258: com > $o] :
      ( ( A_258 = bot_bot_com_o )
     => ~ ( member_com @ A_259 @ A_258 ) ) )).

thf(fact_87_equals0D,axiom,(
    ! [A_259: hoare_1708887482_state,A_258: hoare_1708887482_state > $o] :
      ( ( A_258 = bot_bo19817387tate_o )
     => ~ ( member451959335_state @ A_259 @ A_258 ) ) )).

thf(fact_88_equals0D,axiom,(
    ! [A_259: pname,A_258: pname > $o] :
      ( ( A_258 = bot_bot_pname_o )
     => ~ ( member_pname @ A_259 @ A_258 ) ) )).

thf(fact_89_Collect__empty__eq,axiom,(
    ! [P_44: pname > $o] :
      ( ( ( collect_pname @ P_44 )
        = bot_bot_pname_o )
    <=> ! [X_3: pname] :
          ~ ( P_44 @ X_3 ) ) )).

thf(fact_90_Collect__empty__eq,axiom,(
    ! [P_44: ( pname > $o ) > $o] :
      ( ( ( collect_pname_o @ P_44 )
        = bot_bot_pname_o_o )
    <=> ! [X_3: pname > $o] :
          ~ ( P_44 @ X_3 ) ) )).

thf(fact_91_Collect__empty__eq,axiom,(
    ! [P_44: ( hoare_1708887482_state > $o ) > $o] :
      ( ( ( collec219771562tate_o @ P_44 )
        = bot_bo1678742418te_o_o )
    <=> ! [X_3: hoare_1708887482_state > $o] :
          ~ ( P_44 @ X_3 ) ) )).

thf(fact_92_Collect__empty__eq,axiom,(
    ! [P_44: com > $o] :
      ( ( ( collect_com @ P_44 )
        = bot_bot_com_o )
    <=> ! [X_3: com] :
          ~ ( P_44 @ X_3 ) ) )).

thf(fact_93_Collect__empty__eq,axiom,(
    ! [P_44: hoare_1708887482_state > $o] :
      ( ( ( collec1568722789_state @ P_44 )
        = bot_bo19817387tate_o )
    <=> ! [X_3: hoare_1708887482_state] :
          ~ ( P_44 @ X_3 ) ) )).

thf(fact_94_empty__iff,axiom,(
    ! [C_65: com] :
      ~ ( member_com @ C_65 @ bot_bot_com_o ) )).

thf(fact_95_empty__iff,axiom,(
    ! [C_65: hoare_1708887482_state] :
      ~ ( member451959335_state @ C_65 @ bot_bo19817387tate_o ) )).

thf(fact_96_empty__iff,axiom,(
    ! [C_65: pname] :
      ~ ( member_pname @ C_65 @ bot_bot_pname_o ) )).

thf(fact_97_empty__Collect__eq,axiom,(
    ! [P_43: pname > $o] :
      ( ( bot_bot_pname_o
        = ( collect_pname @ P_43 ) )
    <=> ! [X_3: pname] :
          ~ ( P_43 @ X_3 ) ) )).

thf(fact_98_empty__Collect__eq,axiom,(
    ! [P_43: ( pname > $o ) > $o] :
      ( ( bot_bot_pname_o_o
        = ( collect_pname_o @ P_43 ) )
    <=> ! [X_3: pname > $o] :
          ~ ( P_43 @ X_3 ) ) )).

thf(fact_99_empty__Collect__eq,axiom,(
    ! [P_43: ( hoare_1708887482_state > $o ) > $o] :
      ( ( bot_bo1678742418te_o_o
        = ( collec219771562tate_o @ P_43 ) )
    <=> ! [X_3: hoare_1708887482_state > $o] :
          ~ ( P_43 @ X_3 ) ) )).

thf(fact_100_empty__Collect__eq,axiom,(
    ! [P_43: com > $o] :
      ( ( bot_bot_com_o
        = ( collect_com @ P_43 ) )
    <=> ! [X_3: com] :
          ~ ( P_43 @ X_3 ) ) )).

thf(fact_101_empty__Collect__eq,axiom,(
    ! [P_43: hoare_1708887482_state > $o] :
      ( ( bot_bo19817387tate_o
        = ( collec1568722789_state @ P_43 ) )
    <=> ! [X_3: hoare_1708887482_state] :
          ~ ( P_43 @ X_3 ) ) )).

thf(fact_102_ex__in__conv,axiom,(
    ! [A_257: com > $o] :
      ( ? [X_3: com] :
          ( member_com @ X_3 @ A_257 )
    <=> ( A_257 != bot_bot_com_o ) ) )).

thf(fact_103_ex__in__conv,axiom,(
    ! [A_257: hoare_1708887482_state > $o] :
      ( ? [X_3: hoare_1708887482_state] :
          ( member451959335_state @ X_3 @ A_257 )
    <=> ( A_257 != bot_bo19817387tate_o ) ) )).

thf(fact_104_ex__in__conv,axiom,(
    ! [A_257: pname > $o] :
      ( ? [X_3: pname] :
          ( member_pname @ X_3 @ A_257 )
    <=> ( A_257 != bot_bot_pname_o ) ) )).

thf(fact_105_all__not__in__conv,axiom,(
    ! [A_256: com > $o] :
      ( ! [X_3: com] :
          ~ ( member_com @ X_3 @ A_256 )
    <=> ( A_256 = bot_bot_com_o ) ) )).

thf(fact_106_all__not__in__conv,axiom,(
    ! [A_256: hoare_1708887482_state > $o] :
      ( ! [X_3: hoare_1708887482_state] :
          ~ ( member451959335_state @ X_3 @ A_256 )
    <=> ( A_256 = bot_bo19817387tate_o ) ) )).

thf(fact_107_all__not__in__conv,axiom,(
    ! [A_256: pname > $o] :
      ( ! [X_3: pname] :
          ~ ( member_pname @ X_3 @ A_256 )
    <=> ( A_256 = bot_bot_pname_o ) ) )).

thf(fact_108_empty__def,axiom,
    ( bot_bot_pname_o
    = ( collect_pname
      @ ^ [X_3: pname] : $false ) )).

thf(fact_109_empty__def,axiom,
    ( bot_bot_pname_o_o
    = ( collect_pname_o
      @ ^ [X_3: pname > $o] : $false ) )).

thf(fact_110_empty__def,axiom,
    ( bot_bo1678742418te_o_o
    = ( collec219771562tate_o
      @ ^ [X_3: hoare_1708887482_state > $o] : $false ) )).

thf(fact_111_empty__def,axiom,
    ( bot_bot_com_o
    = ( collect_com
      @ ^ [X_3: com] : $false ) )).

thf(fact_112_empty__def,axiom,
    ( bot_bo19817387tate_o
    = ( collec1568722789_state
      @ ^ [X_3: hoare_1708887482_state] : $false ) )).

thf(fact_113_insert__absorb,axiom,(
    ! [A_255: com,A_254: com > $o] :
      ( ( member_com @ A_255 @ A_254 )
     => ( ( insert_com @ A_255 @ A_254 )
        = A_254 ) ) )).

thf(fact_114_insert__absorb,axiom,(
    ! [A_255: pname,A_254: pname > $o] :
      ( ( member_pname @ A_255 @ A_254 )
     => ( ( insert_pname @ A_255 @ A_254 )
        = A_254 ) ) )).

thf(fact_115_insert__absorb,axiom,(
    ! [A_255: hoare_1708887482_state,A_254: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ A_255 @ A_254 )
     => ( ( insert528405184_state @ A_255 @ A_254 )
        = A_254 ) ) )).

thf(fact_116_insertI2,axiom,(
    ! [B_164: com,A_253: com,B_163: com > $o] :
      ( ( member_com @ A_253 @ B_163 )
     => ( member_com @ A_253 @ ( insert_com @ B_164 @ B_163 ) ) ) )).

thf(fact_117_insertI2,axiom,(
    ! [B_164: pname,A_253: pname,B_163: pname > $o] :
      ( ( member_pname @ A_253 @ B_163 )
     => ( member_pname @ A_253 @ ( insert_pname @ B_164 @ B_163 ) ) ) )).

thf(fact_118_insertI2,axiom,(
    ! [B_164: hoare_1708887482_state,A_253: hoare_1708887482_state,B_163: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ A_253 @ B_163 )
     => ( member451959335_state @ A_253 @ ( insert528405184_state @ B_164 @ B_163 ) ) ) )).

thf(fact_119_insert__ident,axiom,(
    ! [B_162: com > $o,X_115: com,A_252: com > $o] :
      ( ~ ( member_com @ X_115 @ A_252 )
     => ( ~ ( member_com @ X_115 @ B_162 )
       => ( ( ( insert_com @ X_115 @ A_252 )
            = ( insert_com @ X_115 @ B_162 ) )
        <=> ( A_252 = B_162 ) ) ) ) )).

thf(fact_120_insert__ident,axiom,(
    ! [B_162: pname > $o,X_115: pname,A_252: pname > $o] :
      ( ~ ( member_pname @ X_115 @ A_252 )
     => ( ~ ( member_pname @ X_115 @ B_162 )
       => ( ( ( insert_pname @ X_115 @ A_252 )
            = ( insert_pname @ X_115 @ B_162 ) )
        <=> ( A_252 = B_162 ) ) ) ) )).

thf(fact_121_insert__ident,axiom,(
    ! [B_162: hoare_1708887482_state > $o,X_115: hoare_1708887482_state,A_252: hoare_1708887482_state > $o] :
      ( ~ ( member451959335_state @ X_115 @ A_252 )
     => ( ~ ( member451959335_state @ X_115 @ B_162 )
       => ( ( ( insert528405184_state @ X_115 @ A_252 )
            = ( insert528405184_state @ X_115 @ B_162 ) )
        <=> ( A_252 = B_162 ) ) ) ) )).

thf(fact_122_insert__code,axiom,(
    ! [Y_52: pname,A_251: pname > $o,X_114: pname] :
      ( ( insert_pname @ Y_52 @ A_251 @ X_114 )
    <=> ( ( Y_52 = X_114 )
        | ( A_251 @ X_114 ) ) ) )).

thf(fact_123_insert__code,axiom,(
    ! [Y_52: com,A_251: com > $o,X_114: com] :
      ( ( insert_com @ Y_52 @ A_251 @ X_114 )
    <=> ( ( Y_52 = X_114 )
        | ( A_251 @ X_114 ) ) ) )).

thf(fact_124_insert__code,axiom,(
    ! [Y_52: hoare_1708887482_state,A_251: hoare_1708887482_state > $o,X_114: hoare_1708887482_state] :
      ( ( insert528405184_state @ Y_52 @ A_251 @ X_114 )
    <=> ( ( Y_52 = X_114 )
        | ( A_251 @ X_114 ) ) ) )).

thf(fact_125_insert__iff,axiom,(
    ! [A_250: com,B_161: com,A_249: com > $o] :
      ( ( member_com @ A_250 @ ( insert_com @ B_161 @ A_249 ) )
    <=> ( ( A_250 = B_161 )
        | ( member_com @ A_250 @ A_249 ) ) ) )).

thf(fact_126_insert__iff,axiom,(
    ! [A_250: pname,B_161: pname,A_249: pname > $o] :
      ( ( member_pname @ A_250 @ ( insert_pname @ B_161 @ A_249 ) )
    <=> ( ( A_250 = B_161 )
        | ( member_pname @ A_250 @ A_249 ) ) ) )).

thf(fact_127_insert__iff,axiom,(
    ! [A_250: hoare_1708887482_state,B_161: hoare_1708887482_state,A_249: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ A_250 @ ( insert528405184_state @ B_161 @ A_249 ) )
    <=> ( ( A_250 = B_161 )
        | ( member451959335_state @ A_250 @ A_249 ) ) ) )).

thf(fact_128_insert__commute,axiom,(
    ! [X_113: pname,Y_51: pname,A_248: pname > $o] :
      ( ( insert_pname @ X_113 @ ( insert_pname @ Y_51 @ A_248 ) )
      = ( insert_pname @ Y_51 @ ( insert_pname @ X_113 @ A_248 ) ) ) )).

thf(fact_129_insert__commute,axiom,(
    ! [X_113: com,Y_51: com,A_248: com > $o] :
      ( ( insert_com @ X_113 @ ( insert_com @ Y_51 @ A_248 ) )
      = ( insert_com @ Y_51 @ ( insert_com @ X_113 @ A_248 ) ) ) )).

thf(fact_130_insert__commute,axiom,(
    ! [X_113: hoare_1708887482_state,Y_51: hoare_1708887482_state,A_248: hoare_1708887482_state > $o] :
      ( ( insert528405184_state @ X_113 @ ( insert528405184_state @ Y_51 @ A_248 ) )
      = ( insert528405184_state @ Y_51 @ ( insert528405184_state @ X_113 @ A_248 ) ) ) )).

thf(fact_131_insert__absorb2,axiom,(
    ! [X_112: pname,A_247: pname > $o] :
      ( ( insert_pname @ X_112 @ ( insert_pname @ X_112 @ A_247 ) )
      = ( insert_pname @ X_112 @ A_247 ) ) )).

thf(fact_132_insert__absorb2,axiom,(
    ! [X_112: com,A_247: com > $o] :
      ( ( insert_com @ X_112 @ ( insert_com @ X_112 @ A_247 ) )
      = ( insert_com @ X_112 @ A_247 ) ) )).

thf(fact_133_insert__absorb2,axiom,(
    ! [X_112: hoare_1708887482_state,A_247: hoare_1708887482_state > $o] :
      ( ( insert528405184_state @ X_112 @ ( insert528405184_state @ X_112 @ A_247 ) )
      = ( insert528405184_state @ X_112 @ A_247 ) ) )).

thf(fact_134_insert__Collect,axiom,(
    ! [A_246: pname,P_42: pname > $o] :
      ( ( insert_pname @ A_246 @ ( collect_pname @ P_42 ) )
      = ( collect_pname
        @ ^ [U_2: pname] :
            ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) )).

thf(fact_135_insert__Collect,axiom,(
    ! [A_246: com,P_42: com > $o] :
      ( ( insert_com @ A_246 @ ( collect_com @ P_42 ) )
      = ( collect_com
        @ ^ [U_2: com] :
            ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) )).

thf(fact_136_insert__Collect,axiom,(
    ! [A_246: pname > $o,P_42: ( pname > $o ) > $o] :
      ( ( insert_pname_o @ A_246 @ ( collect_pname_o @ P_42 ) )
      = ( collect_pname_o
        @ ^ [U_2: pname > $o] :
            ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) )).

thf(fact_137_insert__Collect,axiom,(
    ! [A_246: hoare_1708887482_state > $o,P_42: ( hoare_1708887482_state > $o ) > $o] :
      ( ( insert949073679tate_o @ A_246 @ ( collec219771562tate_o @ P_42 ) )
      = ( collec219771562tate_o
        @ ^ [U_2: hoare_1708887482_state > $o] :
            ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) )).

thf(fact_138_insert__Collect,axiom,(
    ! [A_246: hoare_1708887482_state,P_42: hoare_1708887482_state > $o] :
      ( ( insert528405184_state @ A_246 @ ( collec1568722789_state @ P_42 ) )
      = ( collec1568722789_state
        @ ^ [U_2: hoare_1708887482_state] :
            ( (=>) @ ( (~) @ ( U_2 = A_246 ) ) @ ( P_42 @ U_2 ) ) ) ) )).

thf(fact_139_insert__compr,axiom,(
    ! [A_245: com,B_160: com > $o] :
      ( ( insert_com @ A_245 @ B_160 )
      = ( collect_com
        @ ^ [X_3: com] :
            ( (|) @ ( X_3 = A_245 ) @ ( member_com @ X_3 @ B_160 ) ) ) ) )).

thf(fact_140_insert__compr,axiom,(
    ! [A_245: pname > $o,B_160: ( pname > $o ) > $o] :
      ( ( insert_pname_o @ A_245 @ B_160 )
      = ( collect_pname_o
        @ ^ [X_3: pname > $o] :
            ( (|) @ ( X_3 = A_245 ) @ ( member_pname_o @ X_3 @ B_160 ) ) ) ) )).

thf(fact_141_insert__compr,axiom,(
    ! [A_245: hoare_1708887482_state > $o,B_160: ( hoare_1708887482_state > $o ) > $o] :
      ( ( insert949073679tate_o @ A_245 @ B_160 )
      = ( collec219771562tate_o
        @ ^ [X_3: hoare_1708887482_state > $o] :
            ( (|) @ ( X_3 = A_245 ) @ ( member814030440tate_o @ X_3 @ B_160 ) ) ) ) )).

thf(fact_142_insert__compr,axiom,(
    ! [A_245: pname,B_160: pname > $o] :
      ( ( insert_pname @ A_245 @ B_160 )
      = ( collect_pname
        @ ^ [X_3: pname] :
            ( (|) @ ( X_3 = A_245 ) @ ( member_pname @ X_3 @ B_160 ) ) ) ) )).

thf(fact_143_insert__compr,axiom,(
    ! [A_245: hoare_1708887482_state,B_160: hoare_1708887482_state > $o] :
      ( ( insert528405184_state @ A_245 @ B_160 )
      = ( collec1568722789_state
        @ ^ [X_3: hoare_1708887482_state] :
            ( (|) @ ( X_3 = A_245 ) @ ( member451959335_state @ X_3 @ B_160 ) ) ) ) )).

thf(fact_144_insertI1,axiom,(
    ! [A_244: com,B_159: com > $o] :
      ( member_com @ A_244 @ ( insert_com @ A_244 @ B_159 ) ) )).

thf(fact_145_insertI1,axiom,(
    ! [A_244: pname,B_159: pname > $o] :
      ( member_pname @ A_244 @ ( insert_pname @ A_244 @ B_159 ) ) )).

thf(fact_146_insertI1,axiom,(
    ! [A_244: hoare_1708887482_state,B_159: hoare_1708887482_state > $o] :
      ( member451959335_state @ A_244 @ ( insert528405184_state @ A_244 @ B_159 ) ) )).

thf(fact_147_equalityE,axiom,(
    ! [A_243: pname > $o,B_158: pname > $o] :
      ( ( A_243 = B_158 )
     => ~ ( ( ord_less_eq_pname_o @ A_243 @ B_158 )
         => ~ ( ord_less_eq_pname_o @ B_158 @ A_243 ) ) ) )).

thf(fact_148_equalityE,axiom,(
    ! [A_243: hoare_1708887482_state > $o,B_158: hoare_1708887482_state > $o] :
      ( ( A_243 = B_158 )
     => ~ ( ( ord_le777019615tate_o @ A_243 @ B_158 )
         => ~ ( ord_le777019615tate_o @ B_158 @ A_243 ) ) ) )).

thf(fact_149_subset__trans,axiom,(
    ! [C_64: pname > $o,A_242: pname > $o,B_157: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_242 @ B_157 )
     => ( ( ord_less_eq_pname_o @ B_157 @ C_64 )
       => ( ord_less_eq_pname_o @ A_242 @ C_64 ) ) ) )).

thf(fact_150_subset__trans,axiom,(
    ! [C_64: hoare_1708887482_state > $o,A_242: hoare_1708887482_state > $o,B_157: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_242 @ B_157 )
     => ( ( ord_le777019615tate_o @ B_157 @ C_64 )
       => ( ord_le777019615tate_o @ A_242 @ C_64 ) ) ) )).

thf(fact_151_set__mp,axiom,(
    ! [X_111: com,A_241: com > $o,B_156: com > $o] :
      ( ( ord_less_eq_com_o @ A_241 @ B_156 )
     => ( ( member_com @ X_111 @ A_241 )
       => ( member_com @ X_111 @ B_156 ) ) ) )).

thf(fact_152_set__mp,axiom,(
    ! [X_111: hoare_1708887482_state,A_241: hoare_1708887482_state > $o,B_156: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_241 @ B_156 )
     => ( ( member451959335_state @ X_111 @ A_241 )
       => ( member451959335_state @ X_111 @ B_156 ) ) ) )).

thf(fact_153_set__mp,axiom,(
    ! [X_111: pname,A_241: pname > $o,B_156: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_241 @ B_156 )
     => ( ( member_pname @ X_111 @ A_241 )
       => ( member_pname @ X_111 @ B_156 ) ) ) )).

thf(fact_154_set__rev__mp,axiom,(
    ! [B_155: com > $o,X_110: com,A_240: com > $o] :
      ( ( member_com @ X_110 @ A_240 )
     => ( ( ord_less_eq_com_o @ A_240 @ B_155 )
       => ( member_com @ X_110 @ B_155 ) ) ) )).

thf(fact_155_set__rev__mp,axiom,(
    ! [B_155: hoare_1708887482_state > $o,X_110: hoare_1708887482_state,A_240: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ X_110 @ A_240 )
     => ( ( ord_le777019615tate_o @ A_240 @ B_155 )
       => ( member451959335_state @ X_110 @ B_155 ) ) ) )).

thf(fact_156_set__rev__mp,axiom,(
    ! [B_155: pname > $o,X_110: pname,A_240: pname > $o] :
      ( ( member_pname @ X_110 @ A_240 )
     => ( ( ord_less_eq_pname_o @ A_240 @ B_155 )
       => ( member_pname @ X_110 @ B_155 ) ) ) )).

thf(fact_157_in__mono,axiom,(
    ! [X_109: com,A_239: com > $o,B_154: com > $o] :
      ( ( ord_less_eq_com_o @ A_239 @ B_154 )
     => ( ( member_com @ X_109 @ A_239 )
       => ( member_com @ X_109 @ B_154 ) ) ) )).

thf(fact_158_in__mono,axiom,(
    ! [X_109: hoare_1708887482_state,A_239: hoare_1708887482_state > $o,B_154: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_239 @ B_154 )
     => ( ( member451959335_state @ X_109 @ A_239 )
       => ( member451959335_state @ X_109 @ B_154 ) ) ) )).

thf(fact_159_in__mono,axiom,(
    ! [X_109: pname,A_239: pname > $o,B_154: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_239 @ B_154 )
     => ( ( member_pname @ X_109 @ A_239 )
       => ( member_pname @ X_109 @ B_154 ) ) ) )).

thf(fact_160_equalityD2,axiom,(
    ! [A_238: pname > $o,B_153: pname > $o] :
      ( ( A_238 = B_153 )
     => ( ord_less_eq_pname_o @ B_153 @ A_238 ) ) )).

thf(fact_161_equalityD2,axiom,(
    ! [A_238: hoare_1708887482_state > $o,B_153: hoare_1708887482_state > $o] :
      ( ( A_238 = B_153 )
     => ( ord_le777019615tate_o @ B_153 @ A_238 ) ) )).

thf(fact_162_equalityD1,axiom,(
    ! [A_237: pname > $o,B_152: pname > $o] :
      ( ( A_237 = B_152 )
     => ( ord_less_eq_pname_o @ A_237 @ B_152 ) ) )).

thf(fact_163_equalityD1,axiom,(
    ! [A_237: hoare_1708887482_state > $o,B_152: hoare_1708887482_state > $o] :
      ( ( A_237 = B_152 )
     => ( ord_le777019615tate_o @ A_237 @ B_152 ) ) )).

thf(fact_164_set__eq__subset,axiom,(
    ! [A_236: pname > $o,B_151: pname > $o] :
      ( ( A_236 = B_151 )
    <=> ( ( ord_less_eq_pname_o @ A_236 @ B_151 )
        & ( ord_less_eq_pname_o @ B_151 @ A_236 ) ) ) )).

thf(fact_165_set__eq__subset,axiom,(
    ! [A_236: hoare_1708887482_state > $o,B_151: hoare_1708887482_state > $o] :
      ( ( A_236 = B_151 )
    <=> ( ( ord_le777019615tate_o @ A_236 @ B_151 )
        & ( ord_le777019615tate_o @ B_151 @ A_236 ) ) ) )).

thf(fact_166_subset__refl,axiom,(
    ! [A_235: pname > $o] :
      ( ord_less_eq_pname_o @ A_235 @ A_235 ) )).

thf(fact_167_subset__refl,axiom,(
    ! [A_235: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ A_235 @ A_235 ) )).

thf(fact_168_rev__image__eqI,axiom,(
    ! [B_150: com,F_84: hoare_1708887482_state > com,X_108: hoare_1708887482_state,A_234: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ X_108 @ A_234 )
     => ( ( B_150
          = ( F_84 @ X_108 ) )
       => ( member_com @ B_150 @ ( image_1604448413te_com @ F_84 @ A_234 ) ) ) ) )).

thf(fact_169_rev__image__eqI,axiom,(
    ! [B_150: com,F_84: pname > com,X_108: pname,A_234: pname > $o] :
      ( ( member_pname @ X_108 @ A_234 )
     => ( ( B_150
          = ( F_84 @ X_108 ) )
       => ( member_com @ B_150 @ ( image_pname_com @ F_84 @ A_234 ) ) ) ) )).

thf(fact_170_rev__image__eqI,axiom,(
    ! [B_150: hoare_1708887482_state,F_84: com > hoare_1708887482_state,X_108: com,A_234: com > $o] :
      ( ( member_com @ X_108 @ A_234 )
     => ( ( B_150
          = ( F_84 @ X_108 ) )
       => ( member451959335_state @ B_150 @ ( image_934102463_state @ F_84 @ A_234 ) ) ) ) )).

thf(fact_171_rev__image__eqI,axiom,(
    ! [B_150: pname,F_84: com > pname,X_108: com,A_234: com > $o] :
      ( ( member_com @ X_108 @ A_234 )
     => ( ( B_150
          = ( F_84 @ X_108 ) )
       => ( member_pname @ B_150 @ ( image_com_pname @ F_84 @ A_234 ) ) ) ) )).

thf(fact_172_rev__image__eqI,axiom,(
    ! [B_150: hoare_1708887482_state,F_84: pname > hoare_1708887482_state,X_108: pname,A_234: pname > $o] :
      ( ( member_pname @ X_108 @ A_234 )
     => ( ( B_150
          = ( F_84 @ X_108 ) )
       => ( member451959335_state @ B_150 @ ( image_1116629049_state @ F_84 @ A_234 ) ) ) ) )).

thf(fact_173_imageI,axiom,(
    ! [F_83: hoare_1708887482_state > com,X_107: hoare_1708887482_state,A_233: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ X_107 @ A_233 )
     => ( member_com @ ( F_83 @ X_107 ) @ ( image_1604448413te_com @ F_83 @ A_233 ) ) ) )).

thf(fact_174_imageI,axiom,(
    ! [F_83: pname > com,X_107: pname,A_233: pname > $o] :
      ( ( member_pname @ X_107 @ A_233 )
     => ( member_com @ ( F_83 @ X_107 ) @ ( image_pname_com @ F_83 @ A_233 ) ) ) )).

thf(fact_175_imageI,axiom,(
    ! [F_83: com > hoare_1708887482_state,X_107: com,A_233: com > $o] :
      ( ( member_com @ X_107 @ A_233 )
     => ( member451959335_state @ ( F_83 @ X_107 ) @ ( image_934102463_state @ F_83 @ A_233 ) ) ) )).

thf(fact_176_imageI,axiom,(
    ! [F_83: com > pname,X_107: com,A_233: com > $o] :
      ( ( member_com @ X_107 @ A_233 )
     => ( member_pname @ ( F_83 @ X_107 ) @ ( image_com_pname @ F_83 @ A_233 ) ) ) )).

thf(fact_177_imageI,axiom,(
    ! [F_83: pname > hoare_1708887482_state,X_107: pname,A_233: pname > $o] :
      ( ( member_pname @ X_107 @ A_233 )
     => ( member451959335_state @ ( F_83 @ X_107 ) @ ( image_1116629049_state @ F_83 @ A_233 ) ) ) )).

thf(fact_178_image__iff,axiom,(
    ! [Z_21: hoare_1708887482_state,F_82: pname > hoare_1708887482_state,A_232: pname > $o] :
      ( ( member451959335_state @ Z_21 @ ( image_1116629049_state @ F_82 @ A_232 ) )
    <=> ? [X_3: pname] :
          ( ( member_pname @ X_3 @ A_232 )
          & ( Z_21
            = ( F_82 @ X_3 ) ) ) ) )).

thf(fact_179_finite__Collect__disjI,axiom,(
    ! [P_41: ( pname > $o ) > $o,Q_25: ( pname > $o ) > $o] :
      ( ( finite297249702name_o
        @ ( collect_pname_o
          @ ^ [X_3: pname > $o] :
              ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
    <=> ( ( finite297249702name_o @ ( collect_pname_o @ P_41 ) )
        & ( finite297249702name_o @ ( collect_pname_o @ Q_25 ) ) ) ) )).

thf(fact_180_finite__Collect__disjI,axiom,(
    ! [P_41: ( hoare_1708887482_state > $o ) > $o,Q_25: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o
        @ ( collec219771562tate_o
          @ ^ [X_3: hoare_1708887482_state > $o] :
              ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
    <=> ( ( finite1329924456tate_o @ ( collec219771562tate_o @ P_41 ) )
        & ( finite1329924456tate_o @ ( collec219771562tate_o @ Q_25 ) ) ) ) )).

thf(fact_181_finite__Collect__disjI,axiom,(
    ! [P_41: hoare_1708887482_state > $o,Q_25: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state
        @ ( collec1568722789_state
          @ ^ [X_3: hoare_1708887482_state] :
              ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
    <=> ( ( finite1625599783_state @ ( collec1568722789_state @ P_41 ) )
        & ( finite1625599783_state @ ( collec1568722789_state @ Q_25 ) ) ) ) )).

thf(fact_182_finite__Collect__disjI,axiom,(
    ! [P_41: pname > $o,Q_25: pname > $o] :
      ( ( finite_finite_pname
        @ ( collect_pname
          @ ^ [X_3: pname] :
              ( (|) @ ( P_41 @ X_3 ) @ ( Q_25 @ X_3 ) ) ) )
    <=> ( ( finite_finite_pname @ ( collect_pname @ P_41 ) )
        & ( finite_finite_pname @ ( collect_pname @ Q_25 ) ) ) ) )).

thf(fact_183_insert__compr__raw,axiom,(
    ! [X_3: com,Xa: com > $o] :
      ( ( insert_com @ X_3 @ Xa )
      = ( collect_com
        @ ^ [Y_4: com] :
            ( (|) @ ( Y_4 = X_3 ) @ ( member_com @ Y_4 @ Xa ) ) ) ) )).

thf(fact_184_insert__compr__raw,axiom,(
    ! [X_3: pname > $o,Xa: ( pname > $o ) > $o] :
      ( ( insert_pname_o @ X_3 @ Xa )
      = ( collect_pname_o
        @ ^ [Y_4: pname > $o] :
            ( (|) @ ( Y_4 = X_3 ) @ ( member_pname_o @ Y_4 @ Xa ) ) ) ) )).

thf(fact_185_insert__compr__raw,axiom,(
    ! [X_3: hoare_1708887482_state > $o,Xa: ( hoare_1708887482_state > $o ) > $o] :
      ( ( insert949073679tate_o @ X_3 @ Xa )
      = ( collec219771562tate_o
        @ ^ [Y_4: hoare_1708887482_state > $o] :
            ( (|) @ ( Y_4 = X_3 ) @ ( member814030440tate_o @ Y_4 @ Xa ) ) ) ) )).

thf(fact_186_insert__compr__raw,axiom,(
    ! [X_3: pname,Xa: pname > $o] :
      ( ( insert_pname @ X_3 @ Xa )
      = ( collect_pname
        @ ^ [Y_4: pname] :
            ( (|) @ ( Y_4 = X_3 ) @ ( member_pname @ Y_4 @ Xa ) ) ) ) )).

thf(fact_187_insert__compr__raw,axiom,(
    ! [X_3: hoare_1708887482_state,Xa: hoare_1708887482_state > $o] :
      ( ( insert528405184_state @ X_3 @ Xa )
      = ( collec1568722789_state
        @ ^ [Y_4: hoare_1708887482_state] :
            ( (|) @ ( Y_4 = X_3 ) @ ( member451959335_state @ Y_4 @ Xa ) ) ) ) )).

thf(fact_188_singleton__inject,axiom,(
    ! [A_231: pname,B_149: pname] :
      ( ( ( insert_pname @ A_231 @ bot_bot_pname_o )
        = ( insert_pname @ B_149 @ bot_bot_pname_o ) )
     => ( A_231 = B_149 ) ) )).

thf(fact_189_singleton__inject,axiom,(
    ! [A_231: com,B_149: com] :
      ( ( ( insert_com @ A_231 @ bot_bot_com_o )
        = ( insert_com @ B_149 @ bot_bot_com_o ) )
     => ( A_231 = B_149 ) ) )).

thf(fact_190_singleton__inject,axiom,(
    ! [A_231: hoare_1708887482_state,B_149: hoare_1708887482_state] :
      ( ( ( insert528405184_state @ A_231 @ bot_bo19817387tate_o )
        = ( insert528405184_state @ B_149 @ bot_bo19817387tate_o ) )
     => ( A_231 = B_149 ) ) )).

thf(fact_191_singletonE,axiom,(
    ! [B_148: com,A_230: com] :
      ( ( member_com @ B_148 @ ( insert_com @ A_230 @ bot_bot_com_o ) )
     => ( B_148 = A_230 ) ) )).

thf(fact_192_singletonE,axiom,(
    ! [B_148: pname,A_230: pname] :
      ( ( member_pname @ B_148 @ ( insert_pname @ A_230 @ bot_bot_pname_o ) )
     => ( B_148 = A_230 ) ) )).

thf(fact_193_singletonE,axiom,(
    ! [B_148: hoare_1708887482_state,A_230: hoare_1708887482_state] :
      ( ( member451959335_state @ B_148 @ ( insert528405184_state @ A_230 @ bot_bo19817387tate_o ) )
     => ( B_148 = A_230 ) ) )).

thf(fact_194_doubleton__eq__iff,axiom,(
    ! [A_229: pname,B_147: pname,C_63: pname,D_7: pname] :
      ( ( ( insert_pname @ A_229 @ ( insert_pname @ B_147 @ bot_bot_pname_o ) )
        = ( insert_pname @ C_63 @ ( insert_pname @ D_7 @ bot_bot_pname_o ) ) )
    <=> ( ( ( A_229 = C_63 )
          & ( B_147 = D_7 ) )
        | ( ( A_229 = D_7 )
          & ( B_147 = C_63 ) ) ) ) )).

thf(fact_195_doubleton__eq__iff,axiom,(
    ! [A_229: com,B_147: com,C_63: com,D_7: com] :
      ( ( ( insert_com @ A_229 @ ( insert_com @ B_147 @ bot_bot_com_o ) )
        = ( insert_com @ C_63 @ ( insert_com @ D_7 @ bot_bot_com_o ) ) )
    <=> ( ( ( A_229 = C_63 )
          & ( B_147 = D_7 ) )
        | ( ( A_229 = D_7 )
          & ( B_147 = C_63 ) ) ) ) )).

thf(fact_196_doubleton__eq__iff,axiom,(
    ! [A_229: hoare_1708887482_state,B_147: hoare_1708887482_state,C_63: hoare_1708887482_state,D_7: hoare_1708887482_state] :
      ( ( ( insert528405184_state @ A_229 @ ( insert528405184_state @ B_147 @ bot_bo19817387tate_o ) )
        = ( insert528405184_state @ C_63 @ ( insert528405184_state @ D_7 @ bot_bo19817387tate_o ) ) )
    <=> ( ( ( A_229 = C_63 )
          & ( B_147 = D_7 ) )
        | ( ( A_229 = D_7 )
          & ( B_147 = C_63 ) ) ) ) )).

thf(fact_197_singleton__iff,axiom,(
    ! [B_146: com,A_228: com] :
      ( ( member_com @ B_146 @ ( insert_com @ A_228 @ bot_bot_com_o ) )
    <=> ( B_146 = A_228 ) ) )).

thf(fact_198_singleton__iff,axiom,(
    ! [B_146: pname,A_228: pname] :
      ( ( member_pname @ B_146 @ ( insert_pname @ A_228 @ bot_bot_pname_o ) )
    <=> ( B_146 = A_228 ) ) )).

thf(fact_199_singleton__iff,axiom,(
    ! [B_146: hoare_1708887482_state,A_228: hoare_1708887482_state] :
      ( ( member451959335_state @ B_146 @ ( insert528405184_state @ A_228 @ bot_bo19817387tate_o ) )
    <=> ( B_146 = A_228 ) ) )).

thf(fact_200_insert__not__empty,axiom,(
    ! [A_227: pname,A_226: pname > $o] :
      ( ( insert_pname @ A_227 @ A_226 )
     != bot_bot_pname_o ) )).

thf(fact_201_insert__not__empty,axiom,(
    ! [A_227: com,A_226: com > $o] :
      ( ( insert_com @ A_227 @ A_226 )
     != bot_bot_com_o ) )).

thf(fact_202_insert__not__empty,axiom,(
    ! [A_227: hoare_1708887482_state,A_226: hoare_1708887482_state > $o] :
      ( ( insert528405184_state @ A_227 @ A_226 )
     != bot_bo19817387tate_o ) )).

thf(fact_203_empty__not__insert,axiom,(
    ! [A_225: pname,A_224: pname > $o] :
      ( bot_bot_pname_o
     != ( insert_pname @ A_225 @ A_224 ) ) )).

thf(fact_204_empty__not__insert,axiom,(
    ! [A_225: com,A_224: com > $o] :
      ( bot_bot_com_o
     != ( insert_com @ A_225 @ A_224 ) ) )).

thf(fact_205_empty__not__insert,axiom,(
    ! [A_225: hoare_1708887482_state,A_224: hoare_1708887482_state > $o] :
      ( bot_bo19817387tate_o
     != ( insert528405184_state @ A_225 @ A_224 ) ) )).

thf(fact_206_finite__insert,axiom,(
    ! [A_223: com,A_222: com > $o] :
      ( ( finite_finite_com @ ( insert_com @ A_223 @ A_222 ) )
    <=> ( finite_finite_com @ A_222 ) ) )).

thf(fact_207_finite__insert,axiom,(
    ! [A_223: pname > $o,A_222: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ ( insert_pname_o @ A_223 @ A_222 ) )
    <=> ( finite297249702name_o @ A_222 ) ) )).

thf(fact_208_finite__insert,axiom,(
    ! [A_223: hoare_1708887482_state > $o,A_222: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ ( insert949073679tate_o @ A_223 @ A_222 ) )
    <=> ( finite1329924456tate_o @ A_222 ) ) )).

thf(fact_209_finite__insert,axiom,(
    ! [A_223: pname,A_222: pname > $o] :
      ( ( finite_finite_pname @ ( insert_pname @ A_223 @ A_222 ) )
    <=> ( finite_finite_pname @ A_222 ) ) )).

thf(fact_210_finite__insert,axiom,(
    ! [A_223: hoare_1708887482_state,A_222: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ ( insert528405184_state @ A_223 @ A_222 ) )
    <=> ( finite1625599783_state @ A_222 ) ) )).

thf(fact_211_subset__empty,axiom,(
    ! [A_221: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_221 @ bot_bot_pname_o )
    <=> ( A_221 = bot_bot_pname_o ) ) )).

thf(fact_212_subset__empty,axiom,(
    ! [A_221: com > $o] :
      ( ( ord_less_eq_com_o @ A_221 @ bot_bot_com_o )
    <=> ( A_221 = bot_bot_com_o ) ) )).

thf(fact_213_subset__empty,axiom,(
    ! [A_221: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_221 @ bot_bo19817387tate_o )
    <=> ( A_221 = bot_bo19817387tate_o ) ) )).

thf(fact_214_image__is__empty,axiom,(
    ! [F_81: com > hoare_1708887482_state,A_220: com > $o] :
      ( ( ( image_934102463_state @ F_81 @ A_220 )
        = bot_bo19817387tate_o )
    <=> ( A_220 = bot_bot_com_o ) ) )).

thf(fact_215_image__is__empty,axiom,(
    ! [F_81: hoare_1708887482_state > pname,A_220: hoare_1708887482_state > $o] :
      ( ( ( image_1509414295_pname @ F_81 @ A_220 )
        = bot_bot_pname_o )
    <=> ( A_220 = bot_bo19817387tate_o ) ) )).

thf(fact_216_image__is__empty,axiom,(
    ! [F_81: hoare_1708887482_state > com,A_220: hoare_1708887482_state > $o] :
      ( ( ( image_1604448413te_com @ F_81 @ A_220 )
        = bot_bot_com_o )
    <=> ( A_220 = bot_bo19817387tate_o ) ) )).

thf(fact_217_image__is__empty,axiom,(
    ! [F_81: pname > hoare_1708887482_state,A_220: pname > $o] :
      ( ( ( image_1116629049_state @ F_81 @ A_220 )
        = bot_bo19817387tate_o )
    <=> ( A_220 = bot_bot_pname_o ) ) )).

thf(fact_218_image__empty,axiom,(
    ! [F_80: hoare_1708887482_state > pname] :
      ( ( image_1509414295_pname @ F_80 @ bot_bo19817387tate_o )
      = bot_bot_pname_o ) )).

thf(fact_219_image__empty,axiom,(
    ! [F_80: hoare_1708887482_state > com] :
      ( ( image_1604448413te_com @ F_80 @ bot_bo19817387tate_o )
      = bot_bot_com_o ) )).

thf(fact_220_image__empty,axiom,(
    ! [F_80: com > hoare_1708887482_state] :
      ( ( image_934102463_state @ F_80 @ bot_bot_com_o )
      = bot_bo19817387tate_o ) )).

thf(fact_221_image__empty,axiom,(
    ! [F_80: pname > hoare_1708887482_state] :
      ( ( image_1116629049_state @ F_80 @ bot_bot_pname_o )
      = bot_bo19817387tate_o ) )).

thf(fact_222_empty__is__image,axiom,(
    ! [F_79: com > hoare_1708887482_state,A_219: com > $o] :
      ( ( bot_bo19817387tate_o
        = ( image_934102463_state @ F_79 @ A_219 ) )
    <=> ( A_219 = bot_bot_com_o ) ) )).

thf(fact_223_empty__is__image,axiom,(
    ! [F_79: hoare_1708887482_state > pname,A_219: hoare_1708887482_state > $o] :
      ( ( bot_bot_pname_o
        = ( image_1509414295_pname @ F_79 @ A_219 ) )
    <=> ( A_219 = bot_bo19817387tate_o ) ) )).

thf(fact_224_empty__is__image,axiom,(
    ! [F_79: hoare_1708887482_state > com,A_219: hoare_1708887482_state > $o] :
      ( ( bot_bot_com_o
        = ( image_1604448413te_com @ F_79 @ A_219 ) )
    <=> ( A_219 = bot_bo19817387tate_o ) ) )).

thf(fact_225_empty__is__image,axiom,(
    ! [F_79: pname > hoare_1708887482_state,A_219: pname > $o] :
      ( ( bot_bo19817387tate_o
        = ( image_1116629049_state @ F_79 @ A_219 ) )
    <=> ( A_219 = bot_bot_pname_o ) ) )).

thf(fact_226_finite__subset,axiom,(
    ! [A_218: ( pname > $o ) > $o,B_145: ( pname > $o ) > $o] :
      ( ( ord_le1205211808me_o_o @ A_218 @ B_145 )
     => ( ( finite297249702name_o @ B_145 )
       => ( finite297249702name_o @ A_218 ) ) ) )).

thf(fact_227_finite__subset,axiom,(
    ! [A_218: ( hoare_1708887482_state > $o ) > $o,B_145: ( hoare_1708887482_state > $o ) > $o] :
      ( ( ord_le1728773982te_o_o @ A_218 @ B_145 )
     => ( ( finite1329924456tate_o @ B_145 )
       => ( finite1329924456tate_o @ A_218 ) ) ) )).

thf(fact_228_finite__subset,axiom,(
    ! [A_218: hoare_1708887482_state > $o,B_145: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_218 @ B_145 )
     => ( ( finite1625599783_state @ B_145 )
       => ( finite1625599783_state @ A_218 ) ) ) )).

thf(fact_229_finite__subset,axiom,(
    ! [A_218: pname > $o,B_145: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_218 @ B_145 )
     => ( ( finite_finite_pname @ B_145 )
       => ( finite_finite_pname @ A_218 ) ) ) )).

thf(fact_230_rev__finite__subset,axiom,(
    ! [A_217: ( pname > $o ) > $o,B_144: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ B_144 )
     => ( ( ord_le1205211808me_o_o @ A_217 @ B_144 )
       => ( finite297249702name_o @ A_217 ) ) ) )).

thf(fact_231_rev__finite__subset,axiom,(
    ! [A_217: ( hoare_1708887482_state > $o ) > $o,B_144: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ B_144 )
     => ( ( ord_le1728773982te_o_o @ A_217 @ B_144 )
       => ( finite1329924456tate_o @ A_217 ) ) ) )).

thf(fact_232_rev__finite__subset,axiom,(
    ! [A_217: hoare_1708887482_state > $o,B_144: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ B_144 )
     => ( ( ord_le777019615tate_o @ A_217 @ B_144 )
       => ( finite1625599783_state @ A_217 ) ) ) )).

thf(fact_233_rev__finite__subset,axiom,(
    ! [A_217: pname > $o,B_144: pname > $o] :
      ( ( finite_finite_pname @ B_144 )
     => ( ( ord_less_eq_pname_o @ A_217 @ B_144 )
       => ( finite_finite_pname @ A_217 ) ) ) )).

thf(fact_234_insert__mono,axiom,(
    ! [A_216: pname,C_62: pname > $o,D_6: pname > $o] :
      ( ( ord_less_eq_pname_o @ C_62 @ D_6 )
     => ( ord_less_eq_pname_o @ ( insert_pname @ A_216 @ C_62 ) @ ( insert_pname @ A_216 @ D_6 ) ) ) )).

thf(fact_235_insert__mono,axiom,(
    ! [A_216: com,C_62: com > $o,D_6: com > $o] :
      ( ( ord_less_eq_com_o @ C_62 @ D_6 )
     => ( ord_less_eq_com_o @ ( insert_com @ A_216 @ C_62 ) @ ( insert_com @ A_216 @ D_6 ) ) ) )).

thf(fact_236_insert__mono,axiom,(
    ! [A_216: hoare_1708887482_state,C_62: hoare_1708887482_state > $o,D_6: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ C_62 @ D_6 )
     => ( ord_le777019615tate_o @ ( insert528405184_state @ A_216 @ C_62 ) @ ( insert528405184_state @ A_216 @ D_6 ) ) ) )).

thf(fact_237_mem__def,axiom,(
    ! [X_106: com,A_215: com > $o] :
      ( ( member_com @ X_106 @ A_215 )
    <=> ( A_215 @ X_106 ) ) )).

thf(fact_238_mem__def,axiom,(
    ! [X_106: hoare_1708887482_state,A_215: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ X_106 @ A_215 )
    <=> ( A_215 @ X_106 ) ) )).

thf(fact_239_mem__def,axiom,(
    ! [X_106: pname,A_215: pname > $o] :
      ( ( member_pname @ X_106 @ A_215 )
    <=> ( A_215 @ X_106 ) ) )).

thf(fact_240_Collect__def,axiom,(
    ! [P_40: hoare_1708887482_state > $o] :
      ( ( collec1568722789_state @ P_40 )
      = P_40 ) )).

thf(fact_241_Collect__def,axiom,(
    ! [P_40: pname > $o] :
      ( ( collect_pname @ P_40 )
      = P_40 ) )).

thf(fact_242_Collect__def,axiom,(
    ! [P_40: ( pname > $o ) > $o] :
      ( ( collect_pname_o @ P_40 )
      = P_40 ) )).

thf(fact_243_Collect__def,axiom,(
    ! [P_40: ( hoare_1708887482_state > $o ) > $o] :
      ( ( collec219771562tate_o @ P_40 )
      = P_40 ) )).

thf(fact_244_subset__insertI2,axiom,(
    ! [B_143: pname,A_214: pname > $o,B_142: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_214 @ B_142 )
     => ( ord_less_eq_pname_o @ A_214 @ ( insert_pname @ B_143 @ B_142 ) ) ) )).

thf(fact_245_subset__insertI2,axiom,(
    ! [B_143: com,A_214: com > $o,B_142: com > $o] :
      ( ( ord_less_eq_com_o @ A_214 @ B_142 )
     => ( ord_less_eq_com_o @ A_214 @ ( insert_com @ B_143 @ B_142 ) ) ) )).

thf(fact_246_subset__insertI2,axiom,(
    ! [B_143: hoare_1708887482_state,A_214: hoare_1708887482_state > $o,B_142: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_214 @ B_142 )
     => ( ord_le777019615tate_o @ A_214 @ ( insert528405184_state @ B_143 @ B_142 ) ) ) )).

thf(fact_247_subset__insert,axiom,(
    ! [B_141: com > $o,X_105: com,A_213: com > $o] :
      ( ~ ( member_com @ X_105 @ A_213 )
     => ( ( ord_less_eq_com_o @ A_213 @ ( insert_com @ X_105 @ B_141 ) )
      <=> ( ord_less_eq_com_o @ A_213 @ B_141 ) ) ) )).

thf(fact_248_subset__insert,axiom,(
    ! [B_141: pname > $o,X_105: pname,A_213: pname > $o] :
      ( ~ ( member_pname @ X_105 @ A_213 )
     => ( ( ord_less_eq_pname_o @ A_213 @ ( insert_pname @ X_105 @ B_141 ) )
      <=> ( ord_less_eq_pname_o @ A_213 @ B_141 ) ) ) )).

thf(fact_249_subset__insert,axiom,(
    ! [B_141: hoare_1708887482_state > $o,X_105: hoare_1708887482_state,A_213: hoare_1708887482_state > $o] :
      ( ~ ( member451959335_state @ X_105 @ A_213 )
     => ( ( ord_le777019615tate_o @ A_213 @ ( insert528405184_state @ X_105 @ B_141 ) )
      <=> ( ord_le777019615tate_o @ A_213 @ B_141 ) ) ) )).

thf(fact_250_insert__subset,axiom,(
    ! [X_104: com,A_212: com > $o,B_140: com > $o] :
      ( ( ord_less_eq_com_o @ ( insert_com @ X_104 @ A_212 ) @ B_140 )
    <=> ( ( member_com @ X_104 @ B_140 )
        & ( ord_less_eq_com_o @ A_212 @ B_140 ) ) ) )).

thf(fact_251_insert__subset,axiom,(
    ! [X_104: pname,A_212: pname > $o,B_140: pname > $o] :
      ( ( ord_less_eq_pname_o @ ( insert_pname @ X_104 @ A_212 ) @ B_140 )
    <=> ( ( member_pname @ X_104 @ B_140 )
        & ( ord_less_eq_pname_o @ A_212 @ B_140 ) ) ) )).

thf(fact_252_insert__subset,axiom,(
    ! [X_104: hoare_1708887482_state,A_212: hoare_1708887482_state > $o,B_140: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ ( insert528405184_state @ X_104 @ A_212 ) @ B_140 )
    <=> ( ( member451959335_state @ X_104 @ B_140 )
        & ( ord_le777019615tate_o @ A_212 @ B_140 ) ) ) )).

thf(fact_253_subset__insertI,axiom,(
    ! [B_139: pname > $o,A_211: pname] :
      ( ord_less_eq_pname_o @ B_139 @ ( insert_pname @ A_211 @ B_139 ) ) )).

thf(fact_254_subset__insertI,axiom,(
    ! [B_139: com > $o,A_211: com] :
      ( ord_less_eq_com_o @ B_139 @ ( insert_com @ A_211 @ B_139 ) ) )).

thf(fact_255_subset__insertI,axiom,(
    ! [B_139: hoare_1708887482_state > $o,A_211: hoare_1708887482_state] :
      ( ord_le777019615tate_o @ B_139 @ ( insert528405184_state @ A_211 @ B_139 ) ) )).

thf(fact_256_insert__image,axiom,(
    ! [F_78: hoare_1708887482_state > pname,X_103: hoare_1708887482_state,A_210: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ X_103 @ A_210 )
     => ( ( insert_pname @ ( F_78 @ X_103 ) @ ( image_1509414295_pname @ F_78 @ A_210 ) )
        = ( image_1509414295_pname @ F_78 @ A_210 ) ) ) )).

thf(fact_257_insert__image,axiom,(
    ! [F_78: hoare_1708887482_state > com,X_103: hoare_1708887482_state,A_210: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ X_103 @ A_210 )
     => ( ( insert_com @ ( F_78 @ X_103 ) @ ( image_1604448413te_com @ F_78 @ A_210 ) )
        = ( image_1604448413te_com @ F_78 @ A_210 ) ) ) )).

thf(fact_258_insert__image,axiom,(
    ! [F_78: pname > pname,X_103: pname,A_210: pname > $o] :
      ( ( member_pname @ X_103 @ A_210 )
     => ( ( insert_pname @ ( F_78 @ X_103 ) @ ( image_pname_pname @ F_78 @ A_210 ) )
        = ( image_pname_pname @ F_78 @ A_210 ) ) ) )).

thf(fact_259_insert__image,axiom,(
    ! [F_78: pname > com,X_103: pname,A_210: pname > $o] :
      ( ( member_pname @ X_103 @ A_210 )
     => ( ( insert_com @ ( F_78 @ X_103 ) @ ( image_pname_com @ F_78 @ A_210 ) )
        = ( image_pname_com @ F_78 @ A_210 ) ) ) )).

thf(fact_260_insert__image,axiom,(
    ! [F_78: com > hoare_1708887482_state,X_103: com,A_210: com > $o] :
      ( ( member_com @ X_103 @ A_210 )
     => ( ( insert528405184_state @ ( F_78 @ X_103 ) @ ( image_934102463_state @ F_78 @ A_210 ) )
        = ( image_934102463_state @ F_78 @ A_210 ) ) ) )).

thf(fact_261_insert__image,axiom,(
    ! [F_78: pname > hoare_1708887482_state,X_103: pname,A_210: pname > $o] :
      ( ( member_pname @ X_103 @ A_210 )
     => ( ( insert528405184_state @ ( F_78 @ X_103 ) @ ( image_1116629049_state @ F_78 @ A_210 ) )
        = ( image_1116629049_state @ F_78 @ A_210 ) ) ) )).

thf(fact_262_image__insert,axiom,(
    ! [F_77: hoare_1708887482_state > pname,A_209: hoare_1708887482_state,B_138: hoare_1708887482_state > $o] :
      ( ( image_1509414295_pname @ F_77 @ ( insert528405184_state @ A_209 @ B_138 ) )
      = ( insert_pname @ ( F_77 @ A_209 ) @ ( image_1509414295_pname @ F_77 @ B_138 ) ) ) )).

thf(fact_263_image__insert,axiom,(
    ! [F_77: hoare_1708887482_state > com,A_209: hoare_1708887482_state,B_138: hoare_1708887482_state > $o] :
      ( ( image_1604448413te_com @ F_77 @ ( insert528405184_state @ A_209 @ B_138 ) )
      = ( insert_com @ ( F_77 @ A_209 ) @ ( image_1604448413te_com @ F_77 @ B_138 ) ) ) )).

thf(fact_264_image__insert,axiom,(
    ! [F_77: com > hoare_1708887482_state,A_209: com,B_138: com > $o] :
      ( ( image_934102463_state @ F_77 @ ( insert_com @ A_209 @ B_138 ) )
      = ( insert528405184_state @ ( F_77 @ A_209 ) @ ( image_934102463_state @ F_77 @ B_138 ) ) ) )).

thf(fact_265_image__insert,axiom,(
    ! [F_77: pname > hoare_1708887482_state,A_209: pname,B_138: pname > $o] :
      ( ( image_1116629049_state @ F_77 @ ( insert_pname @ A_209 @ B_138 ) )
      = ( insert528405184_state @ ( F_77 @ A_209 ) @ ( image_1116629049_state @ F_77 @ B_138 ) ) ) )).

thf(fact_266_image__mono,axiom,(
    ! [F_76: hoare_1708887482_state > pname,A_208: hoare_1708887482_state > $o,B_137: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_208 @ B_137 )
     => ( ord_less_eq_pname_o @ ( image_1509414295_pname @ F_76 @ A_208 ) @ ( image_1509414295_pname @ F_76 @ B_137 ) ) ) )).

thf(fact_267_image__mono,axiom,(
    ! [F_76: pname > hoare_1708887482_state,A_208: pname > $o,B_137: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_208 @ B_137 )
     => ( ord_le777019615tate_o @ ( image_1116629049_state @ F_76 @ A_208 ) @ ( image_1116629049_state @ F_76 @ B_137 ) ) ) )).

thf(fact_268_subset__image__iff,axiom,(
    ! [B_136: pname > $o,F_75: hoare_1708887482_state > pname,A_207: hoare_1708887482_state > $o] :
      ( ( ord_less_eq_pname_o @ B_136 @ ( image_1509414295_pname @ F_75 @ A_207 ) )
    <=> ? [AA: hoare_1708887482_state > $o] :
          ( ( ord_le777019615tate_o @ AA @ A_207 )
          & ( B_136
            = ( image_1509414295_pname @ F_75 @ AA ) ) ) ) )).

thf(fact_269_subset__image__iff,axiom,(
    ! [B_136: hoare_1708887482_state > $o,F_75: pname > hoare_1708887482_state,A_207: pname > $o] :
      ( ( ord_le777019615tate_o @ B_136 @ ( image_1116629049_state @ F_75 @ A_207 ) )
    <=> ? [AA: pname > $o] :
          ( ( ord_less_eq_pname_o @ AA @ A_207 )
          & ( B_136
            = ( image_1116629049_state @ F_75 @ AA ) ) ) ) )).

thf(fact_270_domI,axiom,(
    ! [M_5: com > option_com,A_206: com,B_135: com] :
      ( ( ( M_5 @ A_206 )
        = ( some_com @ B_135 ) )
     => ( member_com @ A_206 @ ( dom_com_com @ M_5 ) ) ) )).

thf(fact_271_domI,axiom,(
    ! [M_5: hoare_1708887482_state > option_pname,A_206: hoare_1708887482_state,B_135: pname] :
      ( ( ( M_5 @ A_206 )
        = ( some_pname @ B_135 ) )
     => ( member451959335_state @ A_206 @ ( dom_Ho1805192458_pname @ M_5 ) ) ) )).

thf(fact_272_domI,axiom,(
    ! [M_5: hoare_1708887482_state > option1624383643_state,A_206: hoare_1708887482_state,B_135: hoare_1708887482_state] :
      ( ( ( M_5 @ A_206 )
        = ( some_H1974565227_state @ B_135 ) )
     => ( member451959335_state @ A_206 @ ( dom_Ho1703271284_state @ M_5 ) ) ) )).

thf(fact_273_domI,axiom,(
    ! [M_5: pname > option_pname,A_206: pname,B_135: pname] :
      ( ( ( M_5 @ A_206 )
        = ( some_pname @ B_135 ) )
     => ( member_pname @ A_206 @ ( dom_pname_pname @ M_5 ) ) ) )).

thf(fact_274_domI,axiom,(
    ! [M_5: pname > option1624383643_state,A_206: pname,B_135: hoare_1708887482_state] :
      ( ( ( M_5 @ A_206 )
        = ( some_H1974565227_state @ B_135 ) )
     => ( member_pname @ A_206 @ ( dom_pn1412407212_state @ M_5 ) ) ) )).

thf(fact_275_domI,axiom,(
    ! [M_5: pname > option_com,A_206: pname,B_135: com] :
      ( ( ( M_5 @ A_206 )
        = ( some_com @ B_135 ) )
     => ( member_pname @ A_206 @ ( dom_pname_com @ M_5 ) ) ) )).

thf(fact_276_Collect__conv__if,axiom,(
    ! [P_39: pname > $o,A_205: pname] :
      ( ( ( P_39 @ A_205 )
       => ( ( collect_pname
            @ ^ [X_3: pname] :
                ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
          = ( insert_pname @ A_205 @ bot_bot_pname_o ) ) )
      & ( ~ ( P_39 @ A_205 )
       => ( ( collect_pname
            @ ^ [X_3: pname] :
                ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
          = bot_bot_pname_o ) ) ) )).

thf(fact_277_Collect__conv__if,axiom,(
    ! [P_39: com > $o,A_205: com] :
      ( ( ( P_39 @ A_205 )
       => ( ( collect_com
            @ ^ [X_3: com] :
                ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
          = ( insert_com @ A_205 @ bot_bot_com_o ) ) )
      & ( ~ ( P_39 @ A_205 )
       => ( ( collect_com
            @ ^ [X_3: com] :
                ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
          = bot_bot_com_o ) ) ) )).

thf(fact_278_Collect__conv__if,axiom,(
    ! [P_39: ( pname > $o ) > $o,A_205: pname > $o] :
      ( ( ( P_39 @ A_205 )
       => ( ( collect_pname_o
            @ ^ [X_3: pname > $o] :
                ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
          = ( insert_pname_o @ A_205 @ bot_bot_pname_o_o ) ) )
      & ( ~ ( P_39 @ A_205 )
       => ( ( collect_pname_o
            @ ^ [X_3: pname > $o] :
                ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
          = bot_bot_pname_o_o ) ) ) )).

thf(fact_279_Collect__conv__if,axiom,(
    ! [P_39: ( hoare_1708887482_state > $o ) > $o,A_205: hoare_1708887482_state > $o] :
      ( ( ( P_39 @ A_205 )
       => ( ( collec219771562tate_o
            @ ^ [X_3: hoare_1708887482_state > $o] :
                ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
          = ( insert949073679tate_o @ A_205 @ bot_bo1678742418te_o_o ) ) )
      & ( ~ ( P_39 @ A_205 )
       => ( ( collec219771562tate_o
            @ ^ [X_3: hoare_1708887482_state > $o] :
                ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
          = bot_bo1678742418te_o_o ) ) ) )).

thf(fact_280_Collect__conv__if,axiom,(
    ! [P_39: hoare_1708887482_state > $o,A_205: hoare_1708887482_state] :
      ( ( ( P_39 @ A_205 )
       => ( ( collec1568722789_state
            @ ^ [X_3: hoare_1708887482_state] :
                ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
          = ( insert528405184_state @ A_205 @ bot_bo19817387tate_o ) ) )
      & ( ~ ( P_39 @ A_205 )
       => ( ( collec1568722789_state
            @ ^ [X_3: hoare_1708887482_state] :
                ( (&) @ ( X_3 = A_205 ) @ ( P_39 @ X_3 ) ) )
          = bot_bo19817387tate_o ) ) ) )).

thf(fact_281_Collect__conv__if2,axiom,(
    ! [P_38: pname > $o,A_204: pname] :
      ( ( ( P_38 @ A_204 )
       => ( ( collect_pname
            @ ^ [X_3: pname] :
                ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
          = ( insert_pname @ A_204 @ bot_bot_pname_o ) ) )
      & ( ~ ( P_38 @ A_204 )
       => ( ( collect_pname
            @ ^ [X_3: pname] :
                ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
          = bot_bot_pname_o ) ) ) )).

thf(fact_282_Collect__conv__if2,axiom,(
    ! [P_38: com > $o,A_204: com] :
      ( ( ( P_38 @ A_204 )
       => ( ( collect_com
            @ ^ [X_3: com] :
                ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
          = ( insert_com @ A_204 @ bot_bot_com_o ) ) )
      & ( ~ ( P_38 @ A_204 )
       => ( ( collect_com
            @ ^ [X_3: com] :
                ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
          = bot_bot_com_o ) ) ) )).

thf(fact_283_Collect__conv__if2,axiom,(
    ! [P_38: ( pname > $o ) > $o,A_204: pname > $o] :
      ( ( ( P_38 @ A_204 )
       => ( ( collect_pname_o
            @ ^ [X_3: pname > $o] :
                ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
          = ( insert_pname_o @ A_204 @ bot_bot_pname_o_o ) ) )
      & ( ~ ( P_38 @ A_204 )
       => ( ( collect_pname_o
            @ ^ [X_3: pname > $o] :
                ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
          = bot_bot_pname_o_o ) ) ) )).

thf(fact_284_Collect__conv__if2,axiom,(
    ! [P_38: ( hoare_1708887482_state > $o ) > $o,A_204: hoare_1708887482_state > $o] :
      ( ( ( P_38 @ A_204 )
       => ( ( collec219771562tate_o
            @ ^ [X_3: hoare_1708887482_state > $o] :
                ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
          = ( insert949073679tate_o @ A_204 @ bot_bo1678742418te_o_o ) ) )
      & ( ~ ( P_38 @ A_204 )
       => ( ( collec219771562tate_o
            @ ^ [X_3: hoare_1708887482_state > $o] :
                ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
          = bot_bo1678742418te_o_o ) ) ) )).

thf(fact_285_Collect__conv__if2,axiom,(
    ! [P_38: hoare_1708887482_state > $o,A_204: hoare_1708887482_state] :
      ( ( ( P_38 @ A_204 )
       => ( ( collec1568722789_state
            @ ^ [X_3: hoare_1708887482_state] :
                ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
          = ( insert528405184_state @ A_204 @ bot_bo19817387tate_o ) ) )
      & ( ~ ( P_38 @ A_204 )
       => ( ( collec1568722789_state
            @ ^ [X_3: hoare_1708887482_state] :
                ( (&) @ ( A_204 = X_3 ) @ ( P_38 @ X_3 ) ) )
          = bot_bo19817387tate_o ) ) ) )).

thf(fact_286_singleton__conv,axiom,(
    ! [A_203: pname] :
      ( ( collect_pname
        @ ^ [X_3: pname] : ( X_3 = A_203 ) )
      = ( insert_pname @ A_203 @ bot_bot_pname_o ) ) )).

thf(fact_287_singleton__conv,axiom,(
    ! [A_203: com] :
      ( ( collect_com
        @ ^ [X_3: com] : ( X_3 = A_203 ) )
      = ( insert_com @ A_203 @ bot_bot_com_o ) ) )).

thf(fact_288_singleton__conv,axiom,(
    ! [A_203: pname > $o] :
      ( ( collect_pname_o
        @ ^ [X_3: pname > $o] : ( X_3 = A_203 ) )
      = ( insert_pname_o @ A_203 @ bot_bot_pname_o_o ) ) )).

thf(fact_289_singleton__conv,axiom,(
    ! [A_203: hoare_1708887482_state > $o] :
      ( ( collec219771562tate_o
        @ ^ [X_3: hoare_1708887482_state > $o] : ( X_3 = A_203 ) )
      = ( insert949073679tate_o @ A_203 @ bot_bo1678742418te_o_o ) ) )).

thf(fact_290_singleton__conv,axiom,(
    ! [A_203: hoare_1708887482_state] :
      ( ( collec1568722789_state
        @ ^ [X_3: hoare_1708887482_state] : ( X_3 = A_203 ) )
      = ( insert528405184_state @ A_203 @ bot_bo19817387tate_o ) ) )).

thf(fact_291_singleton__conv2,axiom,(
    ! [A_202: pname] :
      ( ( collect_pname @ ( fequal_pname @ A_202 ) )
      = ( insert_pname @ A_202 @ bot_bot_pname_o ) ) )).

thf(fact_292_singleton__conv2,axiom,(
    ! [A_202: com] :
      ( ( collect_com @ ( fequal_com @ A_202 ) )
      = ( insert_com @ A_202 @ bot_bot_com_o ) ) )).

thf(fact_293_singleton__conv2,axiom,(
    ! [A_202: pname > $o] :
      ( ( collect_pname_o @ ( fequal_pname_o @ A_202 ) )
      = ( insert_pname_o @ A_202 @ bot_bot_pname_o_o ) ) )).

thf(fact_294_singleton__conv2,axiom,(
    ! [A_202: hoare_1708887482_state > $o] :
      ( ( collec219771562tate_o @ ( fequal1436017556tate_o @ A_202 ) )
      = ( insert949073679tate_o @ A_202 @ bot_bo1678742418te_o_o ) ) )).

thf(fact_295_singleton__conv2,axiom,(
    ! [A_202: hoare_1708887482_state] :
      ( ( collec1568722789_state @ ( fequal224822779_state @ A_202 ) )
      = ( insert528405184_state @ A_202 @ bot_bo19817387tate_o ) ) )).

thf(fact_296_MGF__lemma1,axiom,(
    ! [C_34: com,G_7: hoare_1708887482_state > $o] :
      ( hoare_1160767572gleton
     => ( ! [X_3: pname] :
            ( ( member_pname @ X_3 @ ( dom_pname_com @ body ) )
           => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ ( body_1 @ X_3 ) ) @ bot_bo19817387tate_o ) ) )
       => ( ( wt @ C_34 )
         => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) ) ) ) ) )).

thf(fact_297_WT__bodiesD,axiom,(
    ! [Pn_1: pname,B_82: com] :
      ( wT_bodies
     => ( ( ( body @ Pn_1 )
          = ( some_com @ B_82 ) )
       => ( wt @ B_82 ) ) ) )).

thf(fact_298_imageE,axiom,(
    ! [B_134: hoare_1708887482_state,F_74: com > hoare_1708887482_state,A_201: com > $o] :
      ( ( member451959335_state @ B_134 @ ( image_934102463_state @ F_74 @ A_201 ) )
     => ~ ! [X_3: com] :
            ( ( B_134
              = ( F_74 @ X_3 ) )
           => ~ ( member_com @ X_3 @ A_201 ) ) ) )).

thf(fact_299_imageE,axiom,(
    ! [B_134: pname,F_74: com > pname,A_201: com > $o] :
      ( ( member_pname @ B_134 @ ( image_com_pname @ F_74 @ A_201 ) )
     => ~ ! [X_3: com] :
            ( ( B_134
              = ( F_74 @ X_3 ) )
           => ~ ( member_com @ X_3 @ A_201 ) ) ) )).

thf(fact_300_imageE,axiom,(
    ! [B_134: com,F_74: hoare_1708887482_state > com,A_201: hoare_1708887482_state > $o] :
      ( ( member_com @ B_134 @ ( image_1604448413te_com @ F_74 @ A_201 ) )
     => ~ ! [X_3: hoare_1708887482_state] :
            ( ( B_134
              = ( F_74 @ X_3 ) )
           => ~ ( member451959335_state @ X_3 @ A_201 ) ) ) )).

thf(fact_301_imageE,axiom,(
    ! [B_134: com,F_74: pname > com,A_201: pname > $o] :
      ( ( member_com @ B_134 @ ( image_pname_com @ F_74 @ A_201 ) )
     => ~ ! [X_3: pname] :
            ( ( B_134
              = ( F_74 @ X_3 ) )
           => ~ ( member_pname @ X_3 @ A_201 ) ) ) )).

thf(fact_302_imageE,axiom,(
    ! [B_134: hoare_1708887482_state,F_74: pname > hoare_1708887482_state,A_201: pname > $o] :
      ( ( member451959335_state @ B_134 @ ( image_1116629049_state @ F_74 @ A_201 ) )
     => ~ ! [X_3: pname] :
            ( ( B_134
              = ( F_74 @ X_3 ) )
           => ~ ( member_pname @ X_3 @ A_201 ) ) ) )).

thf(fact_303_finite__subset__induct,axiom,(
    ! [P_37: ( com > $o ) > $o,A_200: com > $o,F_73: com > $o] :
      ( ( finite_finite_com @ F_73 )
     => ( ( ord_less_eq_com_o @ F_73 @ A_200 )
       => ( ( P_37 @ bot_bot_com_o )
         => ( ! [A_6: com,F_53: com > $o] :
                ( ( finite_finite_com @ F_53 )
               => ( ( member_com @ A_6 @ A_200 )
                 => ( ~ ( member_com @ A_6 @ F_53 )
                   => ( ( P_37 @ F_53 )
                     => ( P_37 @ ( insert_com @ A_6 @ F_53 ) ) ) ) ) )
           => ( P_37 @ F_73 ) ) ) ) ) )).

thf(fact_304_finite__subset__induct,axiom,(
    ! [P_37: ( ( pname > $o ) > $o ) > $o,A_200: ( pname > $o ) > $o,F_73: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ F_73 )
     => ( ( ord_le1205211808me_o_o @ F_73 @ A_200 )
       => ( ( P_37 @ bot_bot_pname_o_o )
         => ( ! [A_6: pname > $o,F_53: ( pname > $o ) > $o] :
                ( ( finite297249702name_o @ F_53 )
               => ( ( member_pname_o @ A_6 @ A_200 )
                 => ( ~ ( member_pname_o @ A_6 @ F_53 )
                   => ( ( P_37 @ F_53 )
                     => ( P_37 @ ( insert_pname_o @ A_6 @ F_53 ) ) ) ) ) )
           => ( P_37 @ F_73 ) ) ) ) ) )).

thf(fact_305_finite__subset__induct,axiom,(
    ! [P_37: ( ( hoare_1708887482_state > $o ) > $o ) > $o,A_200: ( hoare_1708887482_state > $o ) > $o,F_73: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ F_73 )
     => ( ( ord_le1728773982te_o_o @ F_73 @ A_200 )
       => ( ( P_37 @ bot_bo1678742418te_o_o )
         => ( ! [A_6: hoare_1708887482_state > $o,F_53: ( hoare_1708887482_state > $o ) > $o] :
                ( ( finite1329924456tate_o @ F_53 )
               => ( ( member814030440tate_o @ A_6 @ A_200 )
                 => ( ~ ( member814030440tate_o @ A_6 @ F_53 )
                   => ( ( P_37 @ F_53 )
                     => ( P_37 @ ( insert949073679tate_o @ A_6 @ F_53 ) ) ) ) ) )
           => ( P_37 @ F_73 ) ) ) ) ) )).

thf(fact_306_finite__subset__induct,axiom,(
    ! [P_37: ( pname > $o ) > $o,A_200: pname > $o,F_73: pname > $o] :
      ( ( finite_finite_pname @ F_73 )
     => ( ( ord_less_eq_pname_o @ F_73 @ A_200 )
       => ( ( P_37 @ bot_bot_pname_o )
         => ( ! [A_6: pname,F_53: pname > $o] :
                ( ( finite_finite_pname @ F_53 )
               => ( ( member_pname @ A_6 @ A_200 )
                 => ( ~ ( member_pname @ A_6 @ F_53 )
                   => ( ( P_37 @ F_53 )
                     => ( P_37 @ ( insert_pname @ A_6 @ F_53 ) ) ) ) ) )
           => ( P_37 @ F_73 ) ) ) ) ) )).

thf(fact_307_finite__subset__induct,axiom,(
    ! [P_37: ( hoare_1708887482_state > $o ) > $o,A_200: hoare_1708887482_state > $o,F_73: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ F_73 )
     => ( ( ord_le777019615tate_o @ F_73 @ A_200 )
       => ( ( P_37 @ bot_bo19817387tate_o )
         => ( ! [A_6: hoare_1708887482_state,F_53: hoare_1708887482_state > $o] :
                ( ( finite1625599783_state @ F_53 )
               => ( ( member451959335_state @ A_6 @ A_200 )
                 => ( ~ ( member451959335_state @ A_6 @ F_53 )
                   => ( ( P_37 @ F_53 )
                     => ( P_37 @ ( insert528405184_state @ A_6 @ F_53 ) ) ) ) ) )
           => ( P_37 @ F_73 ) ) ) ) ) )).

thf(fact_308_WTs__elim__cases_I7_J,axiom,(
    ! [P: pname] :
      ( ( wt @ ( body_1 @ P ) )
     => ~ ! [Y_4: com] :
            ( ( body @ P )
           != ( some_com @ Y_4 ) ) ) )).

thf(fact_309_subsetI,axiom,(
    ! [B_133: com > $o,A_199: com > $o] :
      ( ! [X_3: com] :
          ( ( member_com @ X_3 @ A_199 )
         => ( member_com @ X_3 @ B_133 ) )
     => ( ord_less_eq_com_o @ A_199 @ B_133 ) ) )).

thf(fact_310_subsetI,axiom,(
    ! [B_133: hoare_1708887482_state > $o,A_199: hoare_1708887482_state > $o] :
      ( ! [X_3: hoare_1708887482_state] :
          ( ( member451959335_state @ X_3 @ A_199 )
         => ( member451959335_state @ X_3 @ B_133 ) )
     => ( ord_le777019615tate_o @ A_199 @ B_133 ) ) )).

thf(fact_311_subsetI,axiom,(
    ! [B_133: pname > $o,A_199: pname > $o] :
      ( ! [X_3: pname] :
          ( ( member_pname @ X_3 @ A_199 )
         => ( member_pname @ X_3 @ B_133 ) )
     => ( ord_less_eq_pname_o @ A_199 @ B_133 ) ) )).

thf(fact_312_finite__subset__image,axiom,(
    ! [F_72: ( pname > $o ) > hoare_1708887482_state,A_198: ( pname > $o ) > $o,B_132: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ B_132 )
     => ( ( ord_le777019615tate_o @ B_132 @ ( image_1922967206_state @ F_72 @ A_198 ) )
       => ? [C_61: ( pname > $o ) > $o] :
            ( ( ord_le1205211808me_o_o @ C_61 @ A_198 )
            & ( finite297249702name_o @ C_61 )
            & ( B_132
              = ( image_1922967206_state @ F_72 @ C_61 ) ) ) ) ) )).

thf(fact_313_finite__subset__image,axiom,(
    ! [F_72: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,A_198: ( hoare_1708887482_state > $o ) > $o,B_132: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ B_132 )
     => ( ( ord_le777019615tate_o @ B_132 @ ( image_27005066_state @ F_72 @ A_198 ) )
       => ? [C_61: ( hoare_1708887482_state > $o ) > $o] :
            ( ( ord_le1728773982te_o_o @ C_61 @ A_198 )
            & ( finite1329924456tate_o @ C_61 )
            & ( B_132
              = ( image_27005066_state @ F_72 @ C_61 ) ) ) ) ) )).

thf(fact_314_finite__subset__image,axiom,(
    ! [F_72: ( pname > $o ) > pname,A_198: ( pname > $o ) > $o,B_132: pname > $o] :
      ( ( finite_finite_pname @ B_132 )
     => ( ( ord_less_eq_pname_o @ B_132 @ ( image_pname_o_pname @ F_72 @ A_198 ) )
       => ? [C_61: ( pname > $o ) > $o] :
            ( ( ord_le1205211808me_o_o @ C_61 @ A_198 )
            & ( finite297249702name_o @ C_61 )
            & ( B_132
              = ( image_pname_o_pname @ F_72 @ C_61 ) ) ) ) ) )).

thf(fact_315_finite__subset__image,axiom,(
    ! [F_72: ( hoare_1708887482_state > $o ) > pname,A_198: ( hoare_1708887482_state > $o ) > $o,B_132: pname > $o] :
      ( ( finite_finite_pname @ B_132 )
     => ( ( ord_less_eq_pname_o @ B_132 @ ( image_2051418740_pname @ F_72 @ A_198 ) )
       => ? [C_61: ( hoare_1708887482_state > $o ) > $o] :
            ( ( ord_le1728773982te_o_o @ C_61 @ A_198 )
            & ( finite1329924456tate_o @ C_61 )
            & ( B_132
              = ( image_2051418740_pname @ F_72 @ C_61 ) ) ) ) ) )).

thf(fact_316_finite__subset__image,axiom,(
    ! [F_72: hoare_1708887482_state > pname > $o,A_198: hoare_1708887482_state > $o,B_132: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ B_132 )
     => ( ( ord_le1205211808me_o_o @ B_132 @ ( image_1552895654name_o @ F_72 @ A_198 ) )
       => ? [C_61: hoare_1708887482_state > $o] :
            ( ( ord_le777019615tate_o @ C_61 @ A_198 )
            & ( finite1625599783_state @ C_61 )
            & ( B_132
              = ( image_1552895654name_o @ F_72 @ C_61 ) ) ) ) ) )).

thf(fact_317_finite__subset__image,axiom,(
    ! [F_72: hoare_1708887482_state > hoare_1708887482_state > $o,A_198: hoare_1708887482_state > $o,B_132: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ B_132 )
     => ( ( ord_le1728773982te_o_o @ B_132 @ ( image_1551509096tate_o @ F_72 @ A_198 ) )
       => ? [C_61: hoare_1708887482_state > $o] :
            ( ( ord_le777019615tate_o @ C_61 @ A_198 )
            & ( finite1625599783_state @ C_61 )
            & ( B_132
              = ( image_1551509096tate_o @ F_72 @ C_61 ) ) ) ) ) )).

thf(fact_318_finite__subset__image,axiom,(
    ! [F_72: hoare_1708887482_state > pname,A_198: hoare_1708887482_state > $o,B_132: pname > $o] :
      ( ( finite_finite_pname @ B_132 )
     => ( ( ord_less_eq_pname_o @ B_132 @ ( image_1509414295_pname @ F_72 @ A_198 ) )
       => ? [C_61: hoare_1708887482_state > $o] :
            ( ( ord_le777019615tate_o @ C_61 @ A_198 )
            & ( finite1625599783_state @ C_61 )
            & ( B_132
              = ( image_1509414295_pname @ F_72 @ C_61 ) ) ) ) ) )).

thf(fact_319_finite__subset__image,axiom,(
    ! [F_72: pname > pname > $o,A_198: pname > $o,B_132: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ B_132 )
     => ( ( ord_le1205211808me_o_o @ B_132 @ ( image_pname_pname_o @ F_72 @ A_198 ) )
       => ? [C_61: pname > $o] :
            ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
            & ( finite_finite_pname @ C_61 )
            & ( B_132
              = ( image_pname_pname_o @ F_72 @ C_61 ) ) ) ) ) )).

thf(fact_320_finite__subset__image,axiom,(
    ! [F_72: pname > hoare_1708887482_state > $o,A_198: pname > $o,B_132: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ B_132 )
     => ( ( ord_le1728773982te_o_o @ B_132 @ ( image_425134806tate_o @ F_72 @ A_198 ) )
       => ? [C_61: pname > $o] :
            ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
            & ( finite_finite_pname @ C_61 )
            & ( B_132
              = ( image_425134806tate_o @ F_72 @ C_61 ) ) ) ) ) )).

thf(fact_321_finite__subset__image,axiom,(
    ! [F_72: pname > pname,A_198: pname > $o,B_132: pname > $o] :
      ( ( finite_finite_pname @ B_132 )
     => ( ( ord_less_eq_pname_o @ B_132 @ ( image_pname_pname @ F_72 @ A_198 ) )
       => ? [C_61: pname > $o] :
            ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
            & ( finite_finite_pname @ C_61 )
            & ( B_132
              = ( image_pname_pname @ F_72 @ C_61 ) ) ) ) ) )).

thf(fact_322_finite__subset__image,axiom,(
    ! [F_72: pname > hoare_1708887482_state,A_198: pname > $o,B_132: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ B_132 )
     => ( ( ord_le777019615tate_o @ B_132 @ ( image_1116629049_state @ F_72 @ A_198 ) )
       => ? [C_61: pname > $o] :
            ( ( ord_less_eq_pname_o @ C_61 @ A_198 )
            & ( finite_finite_pname @ C_61 )
            & ( B_132
              = ( image_1116629049_state @ F_72 @ C_61 ) ) ) ) ) )).

thf(fact_323_finite__dom__body,axiom,
    ( finite_finite_pname @ ( dom_pname_com @ body ) )).

thf(fact_324_finite__induct,axiom,(
    ! [P_36: ( com > $o ) > $o,F_71: com > $o] :
      ( ( finite_finite_com @ F_71 )
     => ( ( P_36 @ bot_bot_com_o )
       => ( ! [X_3: com,F_53: com > $o] :
              ( ( finite_finite_com @ F_53 )
             => ( ~ ( member_com @ X_3 @ F_53 )
               => ( ( P_36 @ F_53 )
                 => ( P_36 @ ( insert_com @ X_3 @ F_53 ) ) ) ) )
         => ( P_36 @ F_71 ) ) ) ) )).

thf(fact_325_finite__induct,axiom,(
    ! [P_36: ( ( pname > $o ) > $o ) > $o,F_71: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ F_71 )
     => ( ( P_36 @ bot_bot_pname_o_o )
       => ( ! [X_3: pname > $o,F_53: ( pname > $o ) > $o] :
              ( ( finite297249702name_o @ F_53 )
             => ( ~ ( member_pname_o @ X_3 @ F_53 )
               => ( ( P_36 @ F_53 )
                 => ( P_36 @ ( insert_pname_o @ X_3 @ F_53 ) ) ) ) )
         => ( P_36 @ F_71 ) ) ) ) )).

thf(fact_326_finite__induct,axiom,(
    ! [P_36: ( ( hoare_1708887482_state > $o ) > $o ) > $o,F_71: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ F_71 )
     => ( ( P_36 @ bot_bo1678742418te_o_o )
       => ( ! [X_3: hoare_1708887482_state > $o,F_53: ( hoare_1708887482_state > $o ) > $o] :
              ( ( finite1329924456tate_o @ F_53 )
             => ( ~ ( member814030440tate_o @ X_3 @ F_53 )
               => ( ( P_36 @ F_53 )
                 => ( P_36 @ ( insert949073679tate_o @ X_3 @ F_53 ) ) ) ) )
         => ( P_36 @ F_71 ) ) ) ) )).

thf(fact_327_finite__induct,axiom,(
    ! [P_36: ( pname > $o ) > $o,F_71: pname > $o] :
      ( ( finite_finite_pname @ F_71 )
     => ( ( P_36 @ bot_bot_pname_o )
       => ( ! [X_3: pname,F_53: pname > $o] :
              ( ( finite_finite_pname @ F_53 )
             => ( ~ ( member_pname @ X_3 @ F_53 )
               => ( ( P_36 @ F_53 )
                 => ( P_36 @ ( insert_pname @ X_3 @ F_53 ) ) ) ) )
         => ( P_36 @ F_71 ) ) ) ) )).

thf(fact_328_finite__induct,axiom,(
    ! [P_36: ( hoare_1708887482_state > $o ) > $o,F_71: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ F_71 )
     => ( ( P_36 @ bot_bo19817387tate_o )
       => ( ! [X_3: hoare_1708887482_state,F_53: hoare_1708887482_state > $o] :
              ( ( finite1625599783_state @ F_53 )
             => ( ~ ( member451959335_state @ X_3 @ F_53 )
               => ( ( P_36 @ F_53 )
                 => ( P_36 @ ( insert528405184_state @ X_3 @ F_53 ) ) ) ) )
         => ( P_36 @ F_71 ) ) ) ) )).

thf(fact_329_finite_Osimps,axiom,(
    ! [A_197: com > $o] :
      ( ( finite_finite_com @ A_197 )
    <=> ( ( A_197 = bot_bot_com_o )
        | ? [A_39: com > $o,A_6: com] :
            ( ( A_197
              = ( insert_com @ A_6 @ A_39 ) )
            & ( finite_finite_com @ A_39 ) ) ) ) )).

thf(fact_330_finite_Osimps,axiom,(
    ! [A_197: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_197 )
    <=> ( ( A_197 = bot_bot_pname_o_o )
        | ? [A_39: ( pname > $o ) > $o,A_6: pname > $o] :
            ( ( A_197
              = ( insert_pname_o @ A_6 @ A_39 ) )
            & ( finite297249702name_o @ A_39 ) ) ) ) )).

thf(fact_331_finite_Osimps,axiom,(
    ! [A_197: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_197 )
    <=> ( ( A_197 = bot_bo1678742418te_o_o )
        | ? [A_39: ( hoare_1708887482_state > $o ) > $o,A_6: hoare_1708887482_state > $o] :
            ( ( A_197
              = ( insert949073679tate_o @ A_6 @ A_39 ) )
            & ( finite1329924456tate_o @ A_39 ) ) ) ) )).

thf(fact_332_finite_Osimps,axiom,(
    ! [A_197: pname > $o] :
      ( ( finite_finite_pname @ A_197 )
    <=> ( ( A_197 = bot_bot_pname_o )
        | ? [A_39: pname > $o,A_6: pname] :
            ( ( A_197
              = ( insert_pname @ A_6 @ A_39 ) )
            & ( finite_finite_pname @ A_39 ) ) ) ) )).

thf(fact_333_finite_Osimps,axiom,(
    ! [A_197: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_197 )
    <=> ( ( A_197 = bot_bo19817387tate_o )
        | ? [A_39: hoare_1708887482_state > $o,A_6: hoare_1708887482_state] :
            ( ( A_197
              = ( insert528405184_state @ A_6 @ A_39 ) )
            & ( finite1625599783_state @ A_39 ) ) ) ) )).

thf(fact_334_pigeonhole__infinite,axiom,(
    ! [F_70: com > hoare_1708887482_state,A_196: com > $o] :
      ( ~ ( finite_finite_com @ A_196 )
     => ( ( finite1625599783_state @ ( image_934102463_state @ F_70 @ A_196 ) )
       => ? [X_3: com] :
            ( ( member_com @ X_3 @ A_196 )
            & ~ ( finite_finite_com
                @ ( collect_com
                  @ ^ [A_6: com] :
                      ( (&) @ ( member_com @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_335_pigeonhole__infinite,axiom,(
    ! [F_70: hoare_1708887482_state > hoare_1708887482_state,A_196: hoare_1708887482_state > $o] :
      ( ~ ( finite1625599783_state @ A_196 )
     => ( ( finite1625599783_state @ ( image_757158439_state @ F_70 @ A_196 ) )
       => ? [X_3: hoare_1708887482_state] :
            ( ( member451959335_state @ X_3 @ A_196 )
            & ~ ( finite1625599783_state
                @ ( collec1568722789_state
                  @ ^ [A_6: hoare_1708887482_state] :
                      ( (&) @ ( member451959335_state @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_336_pigeonhole__infinite,axiom,(
    ! [F_70: ( pname > $o ) > hoare_1708887482_state,A_196: ( pname > $o ) > $o] :
      ( ~ ( finite297249702name_o @ A_196 )
     => ( ( finite1625599783_state @ ( image_1922967206_state @ F_70 @ A_196 ) )
       => ? [X_3: pname > $o] :
            ( ( member_pname_o @ X_3 @ A_196 )
            & ~ ( finite297249702name_o
                @ ( collect_pname_o
                  @ ^ [A_6: pname > $o] :
                      ( (&) @ ( member_pname_o @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_337_pigeonhole__infinite,axiom,(
    ! [F_70: ( hoare_1708887482_state > $o ) > hoare_1708887482_state,A_196: ( hoare_1708887482_state > $o ) > $o] :
      ( ~ ( finite1329924456tate_o @ A_196 )
     => ( ( finite1625599783_state @ ( image_27005066_state @ F_70 @ A_196 ) )
       => ? [X_3: hoare_1708887482_state > $o] :
            ( ( member814030440tate_o @ X_3 @ A_196 )
            & ~ ( finite1329924456tate_o
                @ ( collec219771562tate_o
                  @ ^ [A_6: hoare_1708887482_state > $o] :
                      ( (&) @ ( member814030440tate_o @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_338_pigeonhole__infinite,axiom,(
    ! [F_70: com > pname,A_196: com > $o] :
      ( ~ ( finite_finite_com @ A_196 )
     => ( ( finite_finite_pname @ ( image_com_pname @ F_70 @ A_196 ) )
       => ? [X_3: com] :
            ( ( member_com @ X_3 @ A_196 )
            & ~ ( finite_finite_com
                @ ( collect_com
                  @ ^ [A_6: com] :
                      ( (&) @ ( member_com @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_339_pigeonhole__infinite,axiom,(
    ! [F_70: hoare_1708887482_state > pname,A_196: hoare_1708887482_state > $o] :
      ( ~ ( finite1625599783_state @ A_196 )
     => ( ( finite_finite_pname @ ( image_1509414295_pname @ F_70 @ A_196 ) )
       => ? [X_3: hoare_1708887482_state] :
            ( ( member451959335_state @ X_3 @ A_196 )
            & ~ ( finite1625599783_state
                @ ( collec1568722789_state
                  @ ^ [A_6: hoare_1708887482_state] :
                      ( (&) @ ( member451959335_state @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_340_pigeonhole__infinite,axiom,(
    ! [F_70: pname > pname,A_196: pname > $o] :
      ( ~ ( finite_finite_pname @ A_196 )
     => ( ( finite_finite_pname @ ( image_pname_pname @ F_70 @ A_196 ) )
       => ? [X_3: pname] :
            ( ( member_pname @ X_3 @ A_196 )
            & ~ ( finite_finite_pname
                @ ( collect_pname
                  @ ^ [A_6: pname] :
                      ( (&) @ ( member_pname @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_341_pigeonhole__infinite,axiom,(
    ! [F_70: ( pname > $o ) > pname,A_196: ( pname > $o ) > $o] :
      ( ~ ( finite297249702name_o @ A_196 )
     => ( ( finite_finite_pname @ ( image_pname_o_pname @ F_70 @ A_196 ) )
       => ? [X_3: pname > $o] :
            ( ( member_pname_o @ X_3 @ A_196 )
            & ~ ( finite297249702name_o
                @ ( collect_pname_o
                  @ ^ [A_6: pname > $o] :
                      ( (&) @ ( member_pname_o @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_342_pigeonhole__infinite,axiom,(
    ! [F_70: ( hoare_1708887482_state > $o ) > pname,A_196: ( hoare_1708887482_state > $o ) > $o] :
      ( ~ ( finite1329924456tate_o @ A_196 )
     => ( ( finite_finite_pname @ ( image_2051418740_pname @ F_70 @ A_196 ) )
       => ? [X_3: hoare_1708887482_state > $o] :
            ( ( member814030440tate_o @ X_3 @ A_196 )
            & ~ ( finite1329924456tate_o
                @ ( collec219771562tate_o
                  @ ^ [A_6: hoare_1708887482_state > $o] :
                      ( (&) @ ( member814030440tate_o @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_343_pigeonhole__infinite,axiom,(
    ! [F_70: hoare_1708887482_state > pname > $o,A_196: hoare_1708887482_state > $o] :
      ( ~ ( finite1625599783_state @ A_196 )
     => ( ( finite297249702name_o @ ( image_1552895654name_o @ F_70 @ A_196 ) )
       => ? [X_3: hoare_1708887482_state] :
            ( ( member451959335_state @ X_3 @ A_196 )
            & ~ ( finite1625599783_state
                @ ( collec1568722789_state
                  @ ^ [A_6: hoare_1708887482_state] :
                      ( (&) @ ( member451959335_state @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_344_pigeonhole__infinite,axiom,(
    ! [F_70: hoare_1708887482_state > hoare_1708887482_state > $o,A_196: hoare_1708887482_state > $o] :
      ( ~ ( finite1625599783_state @ A_196 )
     => ( ( finite1329924456tate_o @ ( image_1551509096tate_o @ F_70 @ A_196 ) )
       => ? [X_3: hoare_1708887482_state] :
            ( ( member451959335_state @ X_3 @ A_196 )
            & ~ ( finite1625599783_state
                @ ( collec1568722789_state
                  @ ^ [A_6: hoare_1708887482_state] :
                      ( (&) @ ( member451959335_state @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_345_pigeonhole__infinite,axiom,(
    ! [F_70: pname > pname > $o,A_196: pname > $o] :
      ( ~ ( finite_finite_pname @ A_196 )
     => ( ( finite297249702name_o @ ( image_pname_pname_o @ F_70 @ A_196 ) )
       => ? [X_3: pname] :
            ( ( member_pname @ X_3 @ A_196 )
            & ~ ( finite_finite_pname
                @ ( collect_pname
                  @ ^ [A_6: pname] :
                      ( (&) @ ( member_pname @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_346_pigeonhole__infinite,axiom,(
    ! [F_70: pname > hoare_1708887482_state > $o,A_196: pname > $o] :
      ( ~ ( finite_finite_pname @ A_196 )
     => ( ( finite1329924456tate_o @ ( image_425134806tate_o @ F_70 @ A_196 ) )
       => ? [X_3: pname] :
            ( ( member_pname @ X_3 @ A_196 )
            & ~ ( finite_finite_pname
                @ ( collect_pname
                  @ ^ [A_6: pname] :
                      ( (&) @ ( member_pname @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_347_pigeonhole__infinite,axiom,(
    ! [F_70: pname > hoare_1708887482_state,A_196: pname > $o] :
      ( ~ ( finite_finite_pname @ A_196 )
     => ( ( finite1625599783_state @ ( image_1116629049_state @ F_70 @ A_196 ) )
       => ? [X_3: pname] :
            ( ( member_pname @ X_3 @ A_196 )
            & ~ ( finite_finite_pname
                @ ( collect_pname
                  @ ^ [A_6: pname] :
                      ( (&) @ ( member_pname @ A_6 @ A_196 )
                      @ ( ( F_70 @ A_6 )
                        = ( F_70 @ X_3 ) ) ) ) ) ) ) ) )).

thf(fact_348_com_Osimps_I6_J,axiom,(
    ! [Pname_1: pname,Pname: pname] :
      ( ( ( body_1 @ Pname_1 )
        = ( body_1 @ Pname ) )
    <=> ( Pname_1 = Pname ) ) )).

thf(fact_349_MGT__Body,axiom,(
    ! [G_7: hoare_1708887482_state > $o,Procs_3: pname > $o] :
      ( ( hoare_90032982_state
        @ ( semila1122118281tate_o @ G_7
          @ ( image_1116629049_state
            @ ^ [Pn: pname] :
                ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
            @ Procs_3 ) )
        @ ( image_1116629049_state
          @ ^ [Pn: pname] :
              ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
          @ Procs_3 ) )
     => ( ( finite_finite_pname @ Procs_3 )
       => ( hoare_90032982_state @ G_7
          @ ( image_1116629049_state
            @ ^ [Pn: pname] :
                ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
            @ Procs_3 ) ) ) ) )).

thf(fact_350_domD,axiom,(
    ! [A_195: com,M_4: com > option_com] :
      ( ( member_com @ A_195 @ ( dom_com_com @ M_4 ) )
     => ? [B_131: com] :
          ( ( M_4 @ A_195 )
          = ( some_com @ B_131 ) ) ) )).

thf(fact_351_domD,axiom,(
    ! [A_195: hoare_1708887482_state,M_4: hoare_1708887482_state > option_pname] :
      ( ( member451959335_state @ A_195 @ ( dom_Ho1805192458_pname @ M_4 ) )
     => ? [B_131: pname] :
          ( ( M_4 @ A_195 )
          = ( some_pname @ B_131 ) ) ) )).

thf(fact_352_domD,axiom,(
    ! [A_195: hoare_1708887482_state,M_4: hoare_1708887482_state > option1624383643_state] :
      ( ( member451959335_state @ A_195 @ ( dom_Ho1703271284_state @ M_4 ) )
     => ? [B_131: hoare_1708887482_state] :
          ( ( M_4 @ A_195 )
          = ( some_H1974565227_state @ B_131 ) ) ) )).

thf(fact_353_domD,axiom,(
    ! [A_195: pname,M_4: pname > option_pname] :
      ( ( member_pname @ A_195 @ ( dom_pname_pname @ M_4 ) )
     => ? [B_131: pname] :
          ( ( M_4 @ A_195 )
          = ( some_pname @ B_131 ) ) ) )).

thf(fact_354_domD,axiom,(
    ! [A_195: pname,M_4: pname > option1624383643_state] :
      ( ( member_pname @ A_195 @ ( dom_pn1412407212_state @ M_4 ) )
     => ? [B_131: hoare_1708887482_state] :
          ( ( M_4 @ A_195 )
          = ( some_H1974565227_state @ B_131 ) ) ) )).

thf(fact_355_domD,axiom,(
    ! [A_195: pname,M_4: pname > option_com] :
      ( ( member_pname @ A_195 @ ( dom_pname_com @ M_4 ) )
     => ? [B_131: com] :
          ( ( M_4 @ A_195 )
          = ( some_com @ B_131 ) ) ) )).

thf(fact_356_the__elem__eq,axiom,(
    ! [X_102: pname] :
      ( ( the_elem_pname @ ( insert_pname @ X_102 @ bot_bot_pname_o ) )
      = X_102 ) )).

thf(fact_357_the__elem__eq,axiom,(
    ! [X_102: com] :
      ( ( the_elem_com @ ( insert_com @ X_102 @ bot_bot_com_o ) )
      = X_102 ) )).

thf(fact_358_the__elem__eq,axiom,(
    ! [X_102: hoare_1708887482_state] :
      ( ( the_el864710747_state @ ( insert528405184_state @ X_102 @ bot_bo19817387tate_o ) )
      = X_102 ) )).

thf(fact_359_image__subsetI,axiom,(
    ! [F_69: hoare_1708887482_state > com,B_130: com > $o,A_194: hoare_1708887482_state > $o] :
      ( ! [X_3: hoare_1708887482_state] :
          ( ( member451959335_state @ X_3 @ A_194 )
         => ( member_com @ ( F_69 @ X_3 ) @ B_130 ) )
     => ( ord_less_eq_com_o @ ( image_1604448413te_com @ F_69 @ A_194 ) @ B_130 ) ) )).

thf(fact_360_image__subsetI,axiom,(
    ! [F_69: hoare_1708887482_state > pname,B_130: pname > $o,A_194: hoare_1708887482_state > $o] :
      ( ! [X_3: hoare_1708887482_state] :
          ( ( member451959335_state @ X_3 @ A_194 )
         => ( member_pname @ ( F_69 @ X_3 ) @ B_130 ) )
     => ( ord_less_eq_pname_o @ ( image_1509414295_pname @ F_69 @ A_194 ) @ B_130 ) ) )).

thf(fact_361_image__subsetI,axiom,(
    ! [F_69: pname > com,B_130: com > $o,A_194: pname > $o] :
      ( ! [X_3: pname] :
          ( ( member_pname @ X_3 @ A_194 )
         => ( member_com @ ( F_69 @ X_3 ) @ B_130 ) )
     => ( ord_less_eq_com_o @ ( image_pname_com @ F_69 @ A_194 ) @ B_130 ) ) )).

thf(fact_362_image__subsetI,axiom,(
    ! [F_69: pname > pname,B_130: pname > $o,A_194: pname > $o] :
      ( ! [X_3: pname] :
          ( ( member_pname @ X_3 @ A_194 )
         => ( member_pname @ ( F_69 @ X_3 ) @ B_130 ) )
     => ( ord_less_eq_pname_o @ ( image_pname_pname @ F_69 @ A_194 ) @ B_130 ) ) )).

thf(fact_363_image__subsetI,axiom,(
    ! [F_69: com > hoare_1708887482_state,B_130: hoare_1708887482_state > $o,A_194: com > $o] :
      ( ! [X_3: com] :
          ( ( member_com @ X_3 @ A_194 )
         => ( member451959335_state @ ( F_69 @ X_3 ) @ B_130 ) )
     => ( ord_le777019615tate_o @ ( image_934102463_state @ F_69 @ A_194 ) @ B_130 ) ) )).

thf(fact_364_image__subsetI,axiom,(
    ! [F_69: com > pname,B_130: pname > $o,A_194: com > $o] :
      ( ! [X_3: com] :
          ( ( member_com @ X_3 @ A_194 )
         => ( member_pname @ ( F_69 @ X_3 ) @ B_130 ) )
     => ( ord_less_eq_pname_o @ ( image_com_pname @ F_69 @ A_194 ) @ B_130 ) ) )).

thf(fact_365_image__subsetI,axiom,(
    ! [F_69: pname > hoare_1708887482_state,B_130: hoare_1708887482_state > $o,A_194: pname > $o] :
      ( ! [X_3: pname] :
          ( ( member_pname @ X_3 @ A_194 )
         => ( member451959335_state @ ( F_69 @ X_3 ) @ B_130 ) )
     => ( ord_le777019615tate_o @ ( image_1116629049_state @ F_69 @ A_194 ) @ B_130 ) ) )).

thf(fact_366_order__refl,axiom,(
    ! [X_101: pname > $o] :
      ( ord_less_eq_pname_o @ X_101 @ X_101 ) )).

thf(fact_367_order__refl,axiom,(
    ! [X_101: $o] :
      ( ord_less_eq_o @ X_101 @ X_101 ) )).

thf(fact_368_order__refl,axiom,(
    ! [X_101: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ X_101 @ X_101 ) )).

thf(fact_369_nonempty__iff,axiom,(
    ! [A_193: com > $o] :
      ( ( A_193 != bot_bot_com_o )
    <=> ? [X_3: com,B_84: com > $o] :
          ( ( A_193
            = ( insert_com @ X_3 @ B_84 ) )
          & ~ ( member_com @ X_3 @ B_84 ) ) ) )).

thf(fact_370_nonempty__iff,axiom,(
    ! [A_193: pname > $o] :
      ( ( A_193 != bot_bot_pname_o )
    <=> ? [X_3: pname,B_84: pname > $o] :
          ( ( A_193
            = ( insert_pname @ X_3 @ B_84 ) )
          & ~ ( member_pname @ X_3 @ B_84 ) ) ) )).

thf(fact_371_nonempty__iff,axiom,(
    ! [A_193: hoare_1708887482_state > $o] :
      ( ( A_193 != bot_bo19817387tate_o )
    <=> ? [X_3: hoare_1708887482_state,B_84: hoare_1708887482_state > $o] :
          ( ( A_193
            = ( insert528405184_state @ X_3 @ B_84 ) )
          & ~ ( member451959335_state @ X_3 @ B_84 ) ) ) )).

thf(fact_372_the_Osimps,axiom,(
    ! [X_100: pname] :
      ( ( the_pname_1 @ ( some_pname @ X_100 ) )
      = X_100 ) )).

thf(fact_373_the_Osimps,axiom,(
    ! [X_100: hoare_1708887482_state] :
      ( ( the_Ho963921505_state @ ( some_H1974565227_state @ X_100 ) )
      = X_100 ) )).

thf(fact_374_the_Osimps,axiom,(
    ! [X_100: com] :
      ( ( the_com @ ( some_com @ X_100 ) )
      = X_100 ) )).

thf(fact_375_weak__Body,axiom,(
    ! [G_31: hoare_1708887482_state > $o,P_35: state > state > $o,Pn_4: pname,Q_24: state > state > $o] :
      ( ( hoare_90032982_state @ G_31 @ ( insert528405184_state @ ( hoare_858012674_state @ P_35 @ ( the_com @ ( body @ Pn_4 ) ) @ Q_24 ) @ bot_bo19817387tate_o ) )
     => ( hoare_90032982_state @ G_31 @ ( insert528405184_state @ ( hoare_858012674_state @ P_35 @ ( body_1 @ Pn_4 ) @ Q_24 ) @ bot_bo19817387tate_o ) ) ) )).

thf(fact_376_BodyN,axiom,(
    ! [P_34: state > state > $o,Pn_3: pname,Q_23: state > state > $o,G_30: hoare_1708887482_state > $o] :
      ( ( hoare_90032982_state @ ( insert528405184_state @ ( hoare_858012674_state @ P_34 @ ( body_1 @ Pn_3 ) @ Q_23 ) @ G_30 ) @ ( insert528405184_state @ ( hoare_858012674_state @ P_34 @ ( the_com @ ( body @ Pn_3 ) ) @ Q_23 ) @ bot_bo19817387tate_o ) )
     => ( hoare_90032982_state @ G_30 @ ( insert528405184_state @ ( hoare_858012674_state @ P_34 @ ( body_1 @ Pn_3 ) @ Q_23 ) @ bot_bo19817387tate_o ) ) ) )).

thf(fact_377_state__not__singleton__def,axiom,
    ( hoare_1160767572gleton
  <=> ? [S_2: state,T_1: state] : ( S_2 != T_1 ) )).

thf(fact_378_UnCI,axiom,(
    ! [A_192: com > $o,C_60: com,B_129: com > $o] :
      ( ( ~ ( member_com @ C_60 @ B_129 )
       => ( member_com @ C_60 @ A_192 ) )
     => ( member_com @ C_60 @ ( semila1562558655_com_o @ A_192 @ B_129 ) ) ) )).

thf(fact_379_UnCI,axiom,(
    ! [A_192: hoare_1708887482_state > $o,C_60: hoare_1708887482_state,B_129: hoare_1708887482_state > $o] :
      ( ( ~ ( member451959335_state @ C_60 @ B_129 )
       => ( member451959335_state @ C_60 @ A_192 ) )
     => ( member451959335_state @ C_60 @ ( semila1122118281tate_o @ A_192 @ B_129 ) ) ) )).

thf(fact_380_UnCI,axiom,(
    ! [A_192: pname > $o,C_60: pname,B_129: pname > $o] :
      ( ( ~ ( member_pname @ C_60 @ B_129 )
       => ( member_pname @ C_60 @ A_192 ) )
     => ( member_pname @ C_60 @ ( semila1780557381name_o @ A_192 @ B_129 ) ) ) )).

thf(fact_381_UnE,axiom,(
    ! [C_59: com,A_191: com > $o,B_128: com > $o] :
      ( ( member_com @ C_59 @ ( semila1562558655_com_o @ A_191 @ B_128 ) )
     => ( ~ ( member_com @ C_59 @ A_191 )
       => ( member_com @ C_59 @ B_128 ) ) ) )).

thf(fact_382_UnE,axiom,(
    ! [C_59: hoare_1708887482_state,A_191: hoare_1708887482_state > $o,B_128: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_59 @ ( semila1122118281tate_o @ A_191 @ B_128 ) )
     => ( ~ ( member451959335_state @ C_59 @ A_191 )
       => ( member451959335_state @ C_59 @ B_128 ) ) ) )).

thf(fact_383_UnE,axiom,(
    ! [C_59: pname,A_191: pname > $o,B_128: pname > $o] :
      ( ( member_pname @ C_59 @ ( semila1780557381name_o @ A_191 @ B_128 ) )
     => ( ~ ( member_pname @ C_59 @ A_191 )
       => ( member_pname @ C_59 @ B_128 ) ) ) )).

thf(fact_384_triple_Oinject,axiom,(
    ! [Fun1_2: state > state > $o,Com_4: com,Fun2_2: state > state > $o,Fun1_1: state > state > $o,Com_3: com,Fun2_1: state > state > $o] :
      ( ( ( hoare_858012674_state @ Fun1_2 @ Com_4 @ Fun2_2 )
        = ( hoare_858012674_state @ Fun1_1 @ Com_3 @ Fun2_1 ) )
    <=> ( ( Fun1_2 = Fun1_1 )
        & ( Com_4 = Com_3 )
        & ( Fun2_2 = Fun2_1 ) ) ) )).

thf(fact_385_UnI2,axiom,(
    ! [A_190: com > $o,C_58: com,B_127: com > $o] :
      ( ( member_com @ C_58 @ B_127 )
     => ( member_com @ C_58 @ ( semila1562558655_com_o @ A_190 @ B_127 ) ) ) )).

thf(fact_386_UnI2,axiom,(
    ! [A_190: hoare_1708887482_state > $o,C_58: hoare_1708887482_state,B_127: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_58 @ B_127 )
     => ( member451959335_state @ C_58 @ ( semila1122118281tate_o @ A_190 @ B_127 ) ) ) )).

thf(fact_387_UnI2,axiom,(
    ! [A_190: pname > $o,C_58: pname,B_127: pname > $o] :
      ( ( member_pname @ C_58 @ B_127 )
     => ( member_pname @ C_58 @ ( semila1780557381name_o @ A_190 @ B_127 ) ) ) )).

thf(fact_388_UnI1,axiom,(
    ! [B_126: com > $o,C_57: com,A_189: com > $o] :
      ( ( member_com @ C_57 @ A_189 )
     => ( member_com @ C_57 @ ( semila1562558655_com_o @ A_189 @ B_126 ) ) ) )).

thf(fact_389_UnI1,axiom,(
    ! [B_126: hoare_1708887482_state > $o,C_57: hoare_1708887482_state,A_189: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_57 @ A_189 )
     => ( member451959335_state @ C_57 @ ( semila1122118281tate_o @ A_189 @ B_126 ) ) ) )).

thf(fact_390_UnI1,axiom,(
    ! [B_126: pname > $o,C_57: pname,A_189: pname > $o] :
      ( ( member_pname @ C_57 @ A_189 )
     => ( member_pname @ C_57 @ ( semila1780557381name_o @ A_189 @ B_126 ) ) ) )).

thf(fact_391_ball__Un,axiom,(
    ! [P_33: pname > $o,A_188: pname > $o,B_125: pname > $o] :
      ( ! [X_3: pname] :
          ( ( member_pname @ X_3 @ ( semila1780557381name_o @ A_188 @ B_125 ) )
         => ( P_33 @ X_3 ) )
    <=> ( ! [X_3: pname] :
            ( ( member_pname @ X_3 @ A_188 )
           => ( P_33 @ X_3 ) )
        & ! [X_3: pname] :
            ( ( member_pname @ X_3 @ B_125 )
           => ( P_33 @ X_3 ) ) ) ) )).

thf(fact_392_ball__Un,axiom,(
    ! [P_33: hoare_1708887482_state > $o,A_188: hoare_1708887482_state > $o,B_125: hoare_1708887482_state > $o] :
      ( ! [X_3: hoare_1708887482_state] :
          ( ( member451959335_state @ X_3 @ ( semila1122118281tate_o @ A_188 @ B_125 ) )
         => ( P_33 @ X_3 ) )
    <=> ( ! [X_3: hoare_1708887482_state] :
            ( ( member451959335_state @ X_3 @ A_188 )
           => ( P_33 @ X_3 ) )
        & ! [X_3: hoare_1708887482_state] :
            ( ( member451959335_state @ X_3 @ B_125 )
           => ( P_33 @ X_3 ) ) ) ) )).

thf(fact_393_bex__Un,axiom,(
    ! [P_32: pname > $o,A_187: pname > $o,B_124: pname > $o] :
      ( ? [X_3: pname] :
          ( ( member_pname @ X_3 @ ( semila1780557381name_o @ A_187 @ B_124 ) )
          & ( P_32 @ X_3 ) )
    <=> ( ? [X_3: pname] :
            ( ( member_pname @ X_3 @ A_187 )
            & ( P_32 @ X_3 ) )
        | ? [X_3: pname] :
            ( ( member_pname @ X_3 @ B_124 )
            & ( P_32 @ X_3 ) ) ) ) )).

thf(fact_394_bex__Un,axiom,(
    ! [P_32: hoare_1708887482_state > $o,A_187: hoare_1708887482_state > $o,B_124: hoare_1708887482_state > $o] :
      ( ? [X_3: hoare_1708887482_state] :
          ( ( member451959335_state @ X_3 @ ( semila1122118281tate_o @ A_187 @ B_124 ) )
          & ( P_32 @ X_3 ) )
    <=> ( ? [X_3: hoare_1708887482_state] :
            ( ( member451959335_state @ X_3 @ A_187 )
            & ( P_32 @ X_3 ) )
        | ? [X_3: hoare_1708887482_state] :
            ( ( member451959335_state @ X_3 @ B_124 )
            & ( P_32 @ X_3 ) ) ) ) )).

thf(fact_395_Un__assoc,axiom,(
    ! [A_186: pname > $o,B_123: pname > $o,C_56: pname > $o] :
      ( ( semila1780557381name_o @ ( semila1780557381name_o @ A_186 @ B_123 ) @ C_56 )
      = ( semila1780557381name_o @ A_186 @ ( semila1780557381name_o @ B_123 @ C_56 ) ) ) )).

thf(fact_396_Un__assoc,axiom,(
    ! [A_186: hoare_1708887482_state > $o,B_123: hoare_1708887482_state > $o,C_56: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A_186 @ B_123 ) @ C_56 )
      = ( semila1122118281tate_o @ A_186 @ ( semila1122118281tate_o @ B_123 @ C_56 ) ) ) )).

thf(fact_397_Un__iff,axiom,(
    ! [C_55: com,A_185: com > $o,B_122: com > $o] :
      ( ( member_com @ C_55 @ ( semila1562558655_com_o @ A_185 @ B_122 ) )
    <=> ( ( member_com @ C_55 @ A_185 )
        | ( member_com @ C_55 @ B_122 ) ) ) )).

thf(fact_398_Un__iff,axiom,(
    ! [C_55: hoare_1708887482_state,A_185: hoare_1708887482_state > $o,B_122: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_55 @ ( semila1122118281tate_o @ A_185 @ B_122 ) )
    <=> ( ( member451959335_state @ C_55 @ A_185 )
        | ( member451959335_state @ C_55 @ B_122 ) ) ) )).

thf(fact_399_Un__iff,axiom,(
    ! [C_55: pname,A_185: pname > $o,B_122: pname > $o] :
      ( ( member_pname @ C_55 @ ( semila1780557381name_o @ A_185 @ B_122 ) )
    <=> ( ( member_pname @ C_55 @ A_185 )
        | ( member_pname @ C_55 @ B_122 ) ) ) )).

thf(fact_400_Un__left__commute,axiom,(
    ! [A_184: pname > $o,B_121: pname > $o,C_54: pname > $o] :
      ( ( semila1780557381name_o @ A_184 @ ( semila1780557381name_o @ B_121 @ C_54 ) )
      = ( semila1780557381name_o @ B_121 @ ( semila1780557381name_o @ A_184 @ C_54 ) ) ) )).

thf(fact_401_Un__left__commute,axiom,(
    ! [A_184: hoare_1708887482_state > $o,B_121: hoare_1708887482_state > $o,C_54: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_184 @ ( semila1122118281tate_o @ B_121 @ C_54 ) )
      = ( semila1122118281tate_o @ B_121 @ ( semila1122118281tate_o @ A_184 @ C_54 ) ) ) )).

thf(fact_402_Un__left__absorb,axiom,(
    ! [A_183: pname > $o,B_120: pname > $o] :
      ( ( semila1780557381name_o @ A_183 @ ( semila1780557381name_o @ A_183 @ B_120 ) )
      = ( semila1780557381name_o @ A_183 @ B_120 ) ) )).

thf(fact_403_Un__left__absorb,axiom,(
    ! [A_183: hoare_1708887482_state > $o,B_120: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_183 @ ( semila1122118281tate_o @ A_183 @ B_120 ) )
      = ( semila1122118281tate_o @ A_183 @ B_120 ) ) )).

thf(fact_404_Un__commute,axiom,(
    ! [A_182: pname > $o,B_119: pname > $o] :
      ( ( semila1780557381name_o @ A_182 @ B_119 )
      = ( semila1780557381name_o @ B_119 @ A_182 ) ) )).

thf(fact_405_Un__commute,axiom,(
    ! [A_182: hoare_1708887482_state > $o,B_119: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_182 @ B_119 )
      = ( semila1122118281tate_o @ B_119 @ A_182 ) ) )).

thf(fact_406_Un__def,axiom,(
    ! [A_181: com > $o,B_118: com > $o] :
      ( ( semila1562558655_com_o @ A_181 @ B_118 )
      = ( collect_com
        @ ^ [X_3: com] :
            ( (|) @ ( member_com @ X_3 @ A_181 ) @ ( member_com @ X_3 @ B_118 ) ) ) ) )).

thf(fact_407_Un__def,axiom,(
    ! [A_181: ( pname > $o ) > $o,B_118: ( pname > $o ) > $o] :
      ( ( semila181081674me_o_o @ A_181 @ B_118 )
      = ( collect_pname_o
        @ ^ [X_3: pname > $o] :
            ( (|) @ ( member_pname_o @ X_3 @ A_181 ) @ ( member_pname_o @ X_3 @ B_118 ) ) ) ) )).

thf(fact_408_Un__def,axiom,(
    ! [A_181: ( hoare_1708887482_state > $o ) > $o,B_118: ( hoare_1708887482_state > $o ) > $o] :
      ( ( semila1853742644te_o_o @ A_181 @ B_118 )
      = ( collec219771562tate_o
        @ ^ [X_3: hoare_1708887482_state > $o] :
            ( (|) @ ( member814030440tate_o @ X_3 @ A_181 ) @ ( member814030440tate_o @ X_3 @ B_118 ) ) ) ) )).

thf(fact_409_Un__def,axiom,(
    ! [A_181: hoare_1708887482_state > $o,B_118: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_181 @ B_118 )
      = ( collec1568722789_state
        @ ^ [X_3: hoare_1708887482_state] :
            ( (|) @ ( member451959335_state @ X_3 @ A_181 ) @ ( member451959335_state @ X_3 @ B_118 ) ) ) ) )).

thf(fact_410_Un__def,axiom,(
    ! [A_181: pname > $o,B_118: pname > $o] :
      ( ( semila1780557381name_o @ A_181 @ B_118 )
      = ( collect_pname
        @ ^ [X_3: pname] :
            ( (|) @ ( member_pname @ X_3 @ A_181 ) @ ( member_pname @ X_3 @ B_118 ) ) ) ) )).

thf(fact_411_Un__absorb,axiom,(
    ! [A_180: pname > $o] :
      ( ( semila1780557381name_o @ A_180 @ A_180 )
      = A_180 ) )).

thf(fact_412_Un__absorb,axiom,(
    ! [A_180: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_180 @ A_180 )
      = A_180 ) )).

thf(fact_413_Collect__disj__eq,axiom,(
    ! [P_31: pname > $o,Q_22: pname > $o] :
      ( ( collect_pname
        @ ^ [X_3: pname] :
            ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
      = ( semila1780557381name_o @ ( collect_pname @ P_31 ) @ ( collect_pname @ Q_22 ) ) ) )).

thf(fact_414_Collect__disj__eq,axiom,(
    ! [P_31: ( pname > $o ) > $o,Q_22: ( pname > $o ) > $o] :
      ( ( collect_pname_o
        @ ^ [X_3: pname > $o] :
            ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
      = ( semila181081674me_o_o @ ( collect_pname_o @ P_31 ) @ ( collect_pname_o @ Q_22 ) ) ) )).

thf(fact_415_Collect__disj__eq,axiom,(
    ! [P_31: ( hoare_1708887482_state > $o ) > $o,Q_22: ( hoare_1708887482_state > $o ) > $o] :
      ( ( collec219771562tate_o
        @ ^ [X_3: hoare_1708887482_state > $o] :
            ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
      = ( semila1853742644te_o_o @ ( collec219771562tate_o @ P_31 ) @ ( collec219771562tate_o @ Q_22 ) ) ) )).

thf(fact_416_Collect__disj__eq,axiom,(
    ! [P_31: hoare_1708887482_state > $o,Q_22: hoare_1708887482_state > $o] :
      ( ( collec1568722789_state
        @ ^ [X_3: hoare_1708887482_state] :
            ( (|) @ ( P_31 @ X_3 ) @ ( Q_22 @ X_3 ) ) )
      = ( semila1122118281tate_o @ ( collec1568722789_state @ P_31 ) @ ( collec1568722789_state @ Q_22 ) ) ) )).

thf(fact_417_Un__empty,axiom,(
    ! [A_179: pname > $o,B_117: pname > $o] :
      ( ( ( semila1780557381name_o @ A_179 @ B_117 )
        = bot_bot_pname_o )
    <=> ( ( A_179 = bot_bot_pname_o )
        & ( B_117 = bot_bot_pname_o ) ) ) )).

thf(fact_418_Un__empty,axiom,(
    ! [A_179: com > $o,B_117: com > $o] :
      ( ( ( semila1562558655_com_o @ A_179 @ B_117 )
        = bot_bot_com_o )
    <=> ( ( A_179 = bot_bot_com_o )
        & ( B_117 = bot_bot_com_o ) ) ) )).

thf(fact_419_Un__empty,axiom,(
    ! [A_179: hoare_1708887482_state > $o,B_117: hoare_1708887482_state > $o] :
      ( ( ( semila1122118281tate_o @ A_179 @ B_117 )
        = bot_bo19817387tate_o )
    <=> ( ( A_179 = bot_bo19817387tate_o )
        & ( B_117 = bot_bo19817387tate_o ) ) ) )).

thf(fact_420_Un__empty__right,axiom,(
    ! [A_178: pname > $o] :
      ( ( semila1780557381name_o @ A_178 @ bot_bot_pname_o )
      = A_178 ) )).

thf(fact_421_Un__empty__right,axiom,(
    ! [A_178: com > $o] :
      ( ( semila1562558655_com_o @ A_178 @ bot_bot_com_o )
      = A_178 ) )).

thf(fact_422_Un__empty__right,axiom,(
    ! [A_178: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_178 @ bot_bo19817387tate_o )
      = A_178 ) )).

thf(fact_423_Un__empty__left,axiom,(
    ! [B_116: pname > $o] :
      ( ( semila1780557381name_o @ bot_bot_pname_o @ B_116 )
      = B_116 ) )).

thf(fact_424_Un__empty__left,axiom,(
    ! [B_116: com > $o] :
      ( ( semila1562558655_com_o @ bot_bot_com_o @ B_116 )
      = B_116 ) )).

thf(fact_425_Un__empty__left,axiom,(
    ! [B_116: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ bot_bo19817387tate_o @ B_116 )
      = B_116 ) )).

thf(fact_426_finite__UnI,axiom,(
    ! [G_29: ( pname > $o ) > $o,F_68: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ F_68 )
     => ( ( finite297249702name_o @ G_29 )
       => ( finite297249702name_o @ ( semila181081674me_o_o @ F_68 @ G_29 ) ) ) ) )).

thf(fact_427_finite__UnI,axiom,(
    ! [G_29: ( hoare_1708887482_state > $o ) > $o,F_68: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ F_68 )
     => ( ( finite1329924456tate_o @ G_29 )
       => ( finite1329924456tate_o @ ( semila1853742644te_o_o @ F_68 @ G_29 ) ) ) ) )).

thf(fact_428_finite__UnI,axiom,(
    ! [G_29: hoare_1708887482_state > $o,F_68: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ F_68 )
     => ( ( finite1625599783_state @ G_29 )
       => ( finite1625599783_state @ ( semila1122118281tate_o @ F_68 @ G_29 ) ) ) ) )).

thf(fact_429_finite__UnI,axiom,(
    ! [G_29: pname > $o,F_68: pname > $o] :
      ( ( finite_finite_pname @ F_68 )
     => ( ( finite_finite_pname @ G_29 )
       => ( finite_finite_pname @ ( semila1780557381name_o @ F_68 @ G_29 ) ) ) ) )).

thf(fact_430_finite__Un,axiom,(
    ! [F_67: ( pname > $o ) > $o,G_28: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ ( semila181081674me_o_o @ F_67 @ G_28 ) )
    <=> ( ( finite297249702name_o @ F_67 )
        & ( finite297249702name_o @ G_28 ) ) ) )).

thf(fact_431_finite__Un,axiom,(
    ! [F_67: ( hoare_1708887482_state > $o ) > $o,G_28: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ ( semila1853742644te_o_o @ F_67 @ G_28 ) )
    <=> ( ( finite1329924456tate_o @ F_67 )
        & ( finite1329924456tate_o @ G_28 ) ) ) )).

thf(fact_432_finite__Un,axiom,(
    ! [F_67: hoare_1708887482_state > $o,G_28: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ ( semila1122118281tate_o @ F_67 @ G_28 ) )
    <=> ( ( finite1625599783_state @ F_67 )
        & ( finite1625599783_state @ G_28 ) ) ) )).

thf(fact_433_finite__Un,axiom,(
    ! [F_67: pname > $o,G_28: pname > $o] :
      ( ( finite_finite_pname @ ( semila1780557381name_o @ F_67 @ G_28 ) )
    <=> ( ( finite_finite_pname @ F_67 )
        & ( finite_finite_pname @ G_28 ) ) ) )).

thf(fact_434_Un__insert__left,axiom,(
    ! [A_177: pname,B_115: pname > $o,C_53: pname > $o] :
      ( ( semila1780557381name_o @ ( insert_pname @ A_177 @ B_115 ) @ C_53 )
      = ( insert_pname @ A_177 @ ( semila1780557381name_o @ B_115 @ C_53 ) ) ) )).

thf(fact_435_Un__insert__left,axiom,(
    ! [A_177: com,B_115: com > $o,C_53: com > $o] :
      ( ( semila1562558655_com_o @ ( insert_com @ A_177 @ B_115 ) @ C_53 )
      = ( insert_com @ A_177 @ ( semila1562558655_com_o @ B_115 @ C_53 ) ) ) )).

thf(fact_436_Un__insert__left,axiom,(
    ! [A_177: hoare_1708887482_state,B_115: hoare_1708887482_state > $o,C_53: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ ( insert528405184_state @ A_177 @ B_115 ) @ C_53 )
      = ( insert528405184_state @ A_177 @ ( semila1122118281tate_o @ B_115 @ C_53 ) ) ) )).

thf(fact_437_Un__insert__right,axiom,(
    ! [A_176: pname > $o,A_175: pname,B_114: pname > $o] :
      ( ( semila1780557381name_o @ A_176 @ ( insert_pname @ A_175 @ B_114 ) )
      = ( insert_pname @ A_175 @ ( semila1780557381name_o @ A_176 @ B_114 ) ) ) )).

thf(fact_438_Un__insert__right,axiom,(
    ! [A_176: com > $o,A_175: com,B_114: com > $o] :
      ( ( semila1562558655_com_o @ A_176 @ ( insert_com @ A_175 @ B_114 ) )
      = ( insert_com @ A_175 @ ( semila1562558655_com_o @ A_176 @ B_114 ) ) ) )).

thf(fact_439_Un__insert__right,axiom,(
    ! [A_176: hoare_1708887482_state > $o,A_175: hoare_1708887482_state,B_114: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_176 @ ( insert528405184_state @ A_175 @ B_114 ) )
      = ( insert528405184_state @ A_175 @ ( semila1122118281tate_o @ A_176 @ B_114 ) ) ) )).

thf(fact_440_Un__mono,axiom,(
    ! [B_113: pname > $o,D_5: pname > $o,A_174: pname > $o,C_52: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_174 @ C_52 )
     => ( ( ord_less_eq_pname_o @ B_113 @ D_5 )
       => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_174 @ B_113 ) @ ( semila1780557381name_o @ C_52 @ D_5 ) ) ) ) )).

thf(fact_441_Un__mono,axiom,(
    ! [B_113: hoare_1708887482_state > $o,D_5: hoare_1708887482_state > $o,A_174: hoare_1708887482_state > $o,C_52: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_174 @ C_52 )
     => ( ( ord_le777019615tate_o @ B_113 @ D_5 )
       => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_174 @ B_113 ) @ ( semila1122118281tate_o @ C_52 @ D_5 ) ) ) ) )).

thf(fact_442_Un__least,axiom,(
    ! [B_112: pname > $o,A_173: pname > $o,C_51: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_173 @ C_51 )
     => ( ( ord_less_eq_pname_o @ B_112 @ C_51 )
       => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_173 @ B_112 ) @ C_51 ) ) ) )).

thf(fact_443_Un__least,axiom,(
    ! [B_112: hoare_1708887482_state > $o,A_173: hoare_1708887482_state > $o,C_51: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_173 @ C_51 )
     => ( ( ord_le777019615tate_o @ B_112 @ C_51 )
       => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_173 @ B_112 ) @ C_51 ) ) ) )).

thf(fact_444_Un__absorb2,axiom,(
    ! [B_111: pname > $o,A_172: pname > $o] :
      ( ( ord_less_eq_pname_o @ B_111 @ A_172 )
     => ( ( semila1780557381name_o @ A_172 @ B_111 )
        = A_172 ) ) )).

thf(fact_445_Un__absorb2,axiom,(
    ! [B_111: hoare_1708887482_state > $o,A_172: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ B_111 @ A_172 )
     => ( ( semila1122118281tate_o @ A_172 @ B_111 )
        = A_172 ) ) )).

thf(fact_446_Un__absorb1,axiom,(
    ! [A_171: pname > $o,B_110: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_171 @ B_110 )
     => ( ( semila1780557381name_o @ A_171 @ B_110 )
        = B_110 ) ) )).

thf(fact_447_Un__absorb1,axiom,(
    ! [A_171: hoare_1708887482_state > $o,B_110: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_171 @ B_110 )
     => ( ( semila1122118281tate_o @ A_171 @ B_110 )
        = B_110 ) ) )).

thf(fact_448_subset__Un__eq,axiom,(
    ! [A_170: pname > $o,B_109: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_170 @ B_109 )
    <=> ( ( semila1780557381name_o @ A_170 @ B_109 )
        = B_109 ) ) )).

thf(fact_449_subset__Un__eq,axiom,(
    ! [A_170: hoare_1708887482_state > $o,B_109: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_170 @ B_109 )
    <=> ( ( semila1122118281tate_o @ A_170 @ B_109 )
        = B_109 ) ) )).

thf(fact_450_Un__upper2,axiom,(
    ! [B_108: pname > $o,A_169: pname > $o] :
      ( ord_less_eq_pname_o @ B_108 @ ( semila1780557381name_o @ A_169 @ B_108 ) ) )).

thf(fact_451_Un__upper2,axiom,(
    ! [B_108: hoare_1708887482_state > $o,A_169: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ B_108 @ ( semila1122118281tate_o @ A_169 @ B_108 ) ) )).

thf(fact_452_Un__upper1,axiom,(
    ! [A_168: pname > $o,B_107: pname > $o] :
      ( ord_less_eq_pname_o @ A_168 @ ( semila1780557381name_o @ A_168 @ B_107 ) ) )).

thf(fact_453_Un__upper1,axiom,(
    ! [A_168: hoare_1708887482_state > $o,B_107: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ A_168 @ ( semila1122118281tate_o @ A_168 @ B_107 ) ) )).

thf(fact_454_image__Un,axiom,(
    ! [F_66: hoare_1708887482_state > pname,A_167: hoare_1708887482_state > $o,B_106: hoare_1708887482_state > $o] :
      ( ( image_1509414295_pname @ F_66 @ ( semila1122118281tate_o @ A_167 @ B_106 ) )
      = ( semila1780557381name_o @ ( image_1509414295_pname @ F_66 @ A_167 ) @ ( image_1509414295_pname @ F_66 @ B_106 ) ) ) )).

thf(fact_455_image__Un,axiom,(
    ! [F_66: pname > hoare_1708887482_state,A_167: pname > $o,B_106: pname > $o] :
      ( ( image_1116629049_state @ F_66 @ ( semila1780557381name_o @ A_167 @ B_106 ) )
      = ( semila1122118281tate_o @ ( image_1116629049_state @ F_66 @ A_167 ) @ ( image_1116629049_state @ F_66 @ B_106 ) ) ) )).

thf(fact_456_insert__def,axiom,(
    ! [A_166: pname,B_105: pname > $o] :
      ( ( insert_pname @ A_166 @ B_105 )
      = ( semila1780557381name_o
        @ ( collect_pname
          @ ^ [X_3: pname] : ( X_3 = A_166 ) )
        @ B_105 ) ) )).

thf(fact_457_insert__def,axiom,(
    ! [A_166: com,B_105: com > $o] :
      ( ( insert_com @ A_166 @ B_105 )
      = ( semila1562558655_com_o
        @ ( collect_com
          @ ^ [X_3: com] : ( X_3 = A_166 ) )
        @ B_105 ) ) )).

thf(fact_458_insert__def,axiom,(
    ! [A_166: pname > $o,B_105: ( pname > $o ) > $o] :
      ( ( insert_pname_o @ A_166 @ B_105 )
      = ( semila181081674me_o_o
        @ ( collect_pname_o
          @ ^ [X_3: pname > $o] : ( X_3 = A_166 ) )
        @ B_105 ) ) )).

thf(fact_459_insert__def,axiom,(
    ! [A_166: hoare_1708887482_state > $o,B_105: ( hoare_1708887482_state > $o ) > $o] :
      ( ( insert949073679tate_o @ A_166 @ B_105 )
      = ( semila1853742644te_o_o
        @ ( collec219771562tate_o
          @ ^ [X_3: hoare_1708887482_state > $o] : ( X_3 = A_166 ) )
        @ B_105 ) ) )).

thf(fact_460_insert__def,axiom,(
    ! [A_166: hoare_1708887482_state,B_105: hoare_1708887482_state > $o] :
      ( ( insert528405184_state @ A_166 @ B_105 )
      = ( semila1122118281tate_o
        @ ( collec1568722789_state
          @ ^ [X_3: hoare_1708887482_state] : ( X_3 = A_166 ) )
        @ B_105 ) ) )).

thf(fact_461_insert__is__Un,axiom,(
    ! [A_165: pname,A_164: pname > $o] :
      ( ( insert_pname @ A_165 @ A_164 )
      = ( semila1780557381name_o @ ( insert_pname @ A_165 @ bot_bot_pname_o ) @ A_164 ) ) )).

thf(fact_462_insert__is__Un,axiom,(
    ! [A_165: com,A_164: com > $o] :
      ( ( insert_com @ A_165 @ A_164 )
      = ( semila1562558655_com_o @ ( insert_com @ A_165 @ bot_bot_com_o ) @ A_164 ) ) )).

thf(fact_463_insert__is__Un,axiom,(
    ! [A_165: hoare_1708887482_state,A_164: hoare_1708887482_state > $o] :
      ( ( insert528405184_state @ A_165 @ A_164 )
      = ( semila1122118281tate_o @ ( insert528405184_state @ A_165 @ bot_bo19817387tate_o ) @ A_164 ) ) )).

thf(fact_464_hoare__derivs_OBody,axiom,(
    ! [G_27: hoare_1708887482_state > $o,P_30: pname > state > state > $o,Q_21: pname > state > state > $o,Procs_2: pname > $o] :
      ( ( hoare_90032982_state
        @ ( semila1122118281tate_o @ G_27
          @ ( image_1116629049_state
            @ ^ [P_27: pname] :
                ( hoare_858012674_state @ ( P_30 @ P_27 ) @ ( body_1 @ P_27 ) @ ( Q_21 @ P_27 ) )
            @ Procs_2 ) )
        @ ( image_1116629049_state
          @ ^ [P_27: pname] :
              ( hoare_858012674_state @ ( P_30 @ P_27 ) @ ( the_com @ ( body @ P_27 ) ) @ ( Q_21 @ P_27 ) )
          @ Procs_2 ) )
     => ( hoare_90032982_state @ G_27
        @ ( image_1116629049_state
          @ ^ [P_27: pname] :
              ( hoare_858012674_state @ ( P_30 @ P_27 ) @ ( body_1 @ P_27 ) @ ( Q_21 @ P_27 ) )
          @ Procs_2 ) ) ) )).

thf(fact_465_xt1_I6_J,axiom,(
    ! [Z_20: pname > $o,Y_50: pname > $o,X_99: pname > $o] :
      ( ( ord_less_eq_pname_o @ Y_50 @ X_99 )
     => ( ( ord_less_eq_pname_o @ Z_20 @ Y_50 )
       => ( ord_less_eq_pname_o @ Z_20 @ X_99 ) ) ) )).

thf(fact_466_xt1_I6_J,axiom,(
    ! [Z_20: $o,Y_50: $o,X_99: $o] :
      ( ( ord_less_eq_o @ Y_50 @ X_99 )
     => ( ( ord_less_eq_o @ Z_20 @ Y_50 )
       => ( ord_less_eq_o @ Z_20 @ X_99 ) ) ) )).

thf(fact_467_xt1_I6_J,axiom,(
    ! [Z_20: hoare_1708887482_state > $o,Y_50: hoare_1708887482_state > $o,X_99: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ Y_50 @ X_99 )
     => ( ( ord_le777019615tate_o @ Z_20 @ Y_50 )
       => ( ord_le777019615tate_o @ Z_20 @ X_99 ) ) ) )).

thf(fact_468_xt1_I5_J,axiom,(
    ! [Y_49: pname > $o,X_98: pname > $o] :
      ( ( ord_less_eq_pname_o @ Y_49 @ X_98 )
     => ( ( ord_less_eq_pname_o @ X_98 @ Y_49 )
       => ( X_98 = Y_49 ) ) ) )).

thf(fact_469_xt1_I5_J,axiom,(
    ! [Y_49: $o,X_98: $o] :
      ( ( ord_less_eq_o @ Y_49 @ X_98 )
     => ( ( ord_less_eq_o @ X_98 @ Y_49 )
       => ( X_98
        <=> Y_49 ) ) ) )).

thf(fact_470_xt1_I5_J,axiom,(
    ! [Y_49: hoare_1708887482_state > $o,X_98: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ Y_49 @ X_98 )
     => ( ( ord_le777019615tate_o @ X_98 @ Y_49 )
       => ( X_98 = Y_49 ) ) ) )).

thf(fact_471_order__trans,axiom,(
    ! [Z_19: pname > $o,X_97: pname > $o,Y_48: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_97 @ Y_48 )
     => ( ( ord_less_eq_pname_o @ Y_48 @ Z_19 )
       => ( ord_less_eq_pname_o @ X_97 @ Z_19 ) ) ) )).

thf(fact_472_order__trans,axiom,(
    ! [Z_19: $o,X_97: $o,Y_48: $o] :
      ( ( ord_less_eq_o @ X_97 @ Y_48 )
     => ( ( ord_less_eq_o @ Y_48 @ Z_19 )
       => ( ord_less_eq_o @ X_97 @ Z_19 ) ) ) )).

thf(fact_473_order__trans,axiom,(
    ! [Z_19: hoare_1708887482_state > $o,X_97: hoare_1708887482_state > $o,Y_48: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_97 @ Y_48 )
     => ( ( ord_le777019615tate_o @ Y_48 @ Z_19 )
       => ( ord_le777019615tate_o @ X_97 @ Z_19 ) ) ) )).

thf(fact_474_order__antisym,axiom,(
    ! [X_96: pname > $o,Y_47: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_96 @ Y_47 )
     => ( ( ord_less_eq_pname_o @ Y_47 @ X_96 )
       => ( X_96 = Y_47 ) ) ) )).

thf(fact_475_order__antisym,axiom,(
    ! [X_96: $o,Y_47: $o] :
      ( ( ord_less_eq_o @ X_96 @ Y_47 )
     => ( ( ord_less_eq_o @ Y_47 @ X_96 )
       => ( X_96
        <=> Y_47 ) ) ) )).

thf(fact_476_order__antisym,axiom,(
    ! [X_96: hoare_1708887482_state > $o,Y_47: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_96 @ Y_47 )
     => ( ( ord_le777019615tate_o @ Y_47 @ X_96 )
       => ( X_96 = Y_47 ) ) ) )).

thf(fact_477_xt1_I4_J,axiom,(
    ! [C_50: pname > $o,B_104: pname > $o,A_163: pname > $o] :
      ( ( ord_less_eq_pname_o @ B_104 @ A_163 )
     => ( ( B_104 = C_50 )
       => ( ord_less_eq_pname_o @ C_50 @ A_163 ) ) ) )).

thf(fact_478_xt1_I4_J,axiom,(
    ! [C_50: $o,B_104: $o,A_163: $o] :
      ( ( ord_less_eq_o @ B_104 @ A_163 )
     => ( ( B_104
        <=> C_50 )
       => ( ord_less_eq_o @ C_50 @ A_163 ) ) ) )).

thf(fact_479_xt1_I4_J,axiom,(
    ! [C_50: hoare_1708887482_state > $o,B_104: hoare_1708887482_state > $o,A_163: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ B_104 @ A_163 )
     => ( ( B_104 = C_50 )
       => ( ord_le777019615tate_o @ C_50 @ A_163 ) ) ) )).

thf(fact_480_ord__le__eq__trans,axiom,(
    ! [C_49: pname > $o,A_162: pname > $o,B_103: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_162 @ B_103 )
     => ( ( B_103 = C_49 )
       => ( ord_less_eq_pname_o @ A_162 @ C_49 ) ) ) )).

thf(fact_481_ord__le__eq__trans,axiom,(
    ! [C_49: $o,A_162: $o,B_103: $o] :
      ( ( ord_less_eq_o @ A_162 @ B_103 )
     => ( ( B_103
        <=> C_49 )
       => ( ord_less_eq_o @ A_162 @ C_49 ) ) ) )).

thf(fact_482_ord__le__eq__trans,axiom,(
    ! [C_49: hoare_1708887482_state > $o,A_162: hoare_1708887482_state > $o,B_103: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_162 @ B_103 )
     => ( ( B_103 = C_49 )
       => ( ord_le777019615tate_o @ A_162 @ C_49 ) ) ) )).

thf(fact_483_xt1_I3_J,axiom,(
    ! [C_48: pname > $o,A_161: pname > $o,B_102: pname > $o] :
      ( ( A_161 = B_102 )
     => ( ( ord_less_eq_pname_o @ C_48 @ B_102 )
       => ( ord_less_eq_pname_o @ C_48 @ A_161 ) ) ) )).

thf(fact_484_xt1_I3_J,axiom,(
    ! [C_48: $o,B_102: $o,A_161: $o] :
      ( ( A_161
      <=> B_102 )
     => ( ( ord_less_eq_o @ C_48 @ B_102 )
       => ( ord_less_eq_o @ C_48 @ A_161 ) ) ) )).

thf(fact_485_xt1_I3_J,axiom,(
    ! [C_48: hoare_1708887482_state > $o,A_161: hoare_1708887482_state > $o,B_102: hoare_1708887482_state > $o] :
      ( ( A_161 = B_102 )
     => ( ( ord_le777019615tate_o @ C_48 @ B_102 )
       => ( ord_le777019615tate_o @ C_48 @ A_161 ) ) ) )).

thf(fact_486_ord__eq__le__trans,axiom,(
    ! [C_47: pname > $o,A_160: pname > $o,B_101: pname > $o] :
      ( ( A_160 = B_101 )
     => ( ( ord_less_eq_pname_o @ B_101 @ C_47 )
       => ( ord_less_eq_pname_o @ A_160 @ C_47 ) ) ) )).

thf(fact_487_ord__eq__le__trans,axiom,(
    ! [C_47: $o,B_101: $o,A_160: $o] :
      ( ( A_160
      <=> B_101 )
     => ( ( ord_less_eq_o @ B_101 @ C_47 )
       => ( ord_less_eq_o @ A_160 @ C_47 ) ) ) )).

thf(fact_488_ord__eq__le__trans,axiom,(
    ! [C_47: hoare_1708887482_state > $o,A_160: hoare_1708887482_state > $o,B_101: hoare_1708887482_state > $o] :
      ( ( A_160 = B_101 )
     => ( ( ord_le777019615tate_o @ B_101 @ C_47 )
       => ( ord_le777019615tate_o @ A_160 @ C_47 ) ) ) )).

thf(fact_489_order__antisym__conv,axiom,(
    ! [Y_46: pname > $o,X_95: pname > $o] :
      ( ( ord_less_eq_pname_o @ Y_46 @ X_95 )
     => ( ( ord_less_eq_pname_o @ X_95 @ Y_46 )
      <=> ( X_95 = Y_46 ) ) ) )).

thf(fact_490_order__antisym__conv,axiom,(
    ! [Y_46: $o,X_95: $o] :
      ( ( ord_less_eq_o @ Y_46 @ X_95 )
     => ( ( ord_less_eq_o @ X_95 @ Y_46 )
      <=> ( X_95
        <=> Y_46 ) ) ) )).

thf(fact_491_order__antisym__conv,axiom,(
    ! [Y_46: hoare_1708887482_state > $o,X_95: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ Y_46 @ X_95 )
     => ( ( ord_le777019615tate_o @ X_95 @ Y_46 )
      <=> ( X_95 = Y_46 ) ) ) )).

thf(fact_492_order__eq__refl,axiom,(
    ! [X_94: pname > $o,Y_45: pname > $o] :
      ( ( X_94 = Y_45 )
     => ( ord_less_eq_pname_o @ X_94 @ Y_45 ) ) )).

thf(fact_493_order__eq__refl,axiom,(
    ! [Y_45: $o,X_94: $o] :
      ( ( X_94
      <=> Y_45 )
     => ( ord_less_eq_o @ X_94 @ Y_45 ) ) )).

thf(fact_494_order__eq__refl,axiom,(
    ! [X_94: hoare_1708887482_state > $o,Y_45: hoare_1708887482_state > $o] :
      ( ( X_94 = Y_45 )
     => ( ord_le777019615tate_o @ X_94 @ Y_45 ) ) )).

thf(fact_495_order__eq__iff,axiom,(
    ! [X_93: pname > $o,Y_44: pname > $o] :
      ( ( X_93 = Y_44 )
    <=> ( ( ord_less_eq_pname_o @ X_93 @ Y_44 )
        & ( ord_less_eq_pname_o @ Y_44 @ X_93 ) ) ) )).

thf(fact_496_order__eq__iff,axiom,(
    ! [Y_44: $o,X_93: $o] :
      ( ( X_93
      <=> Y_44 )
    <=> ( ( ord_less_eq_o @ X_93 @ Y_44 )
        & ( ord_less_eq_o @ Y_44 @ X_93 ) ) ) )).

thf(fact_497_order__eq__iff,axiom,(
    ! [X_93: hoare_1708887482_state > $o,Y_44: hoare_1708887482_state > $o] :
      ( ( X_93 = Y_44 )
    <=> ( ( ord_le777019615tate_o @ X_93 @ Y_44 )
        & ( ord_le777019615tate_o @ Y_44 @ X_93 ) ) ) )).

thf(fact_498_option_Oinject,axiom,(
    ! [A_159: pname,A_158: pname] :
      ( ( ( some_pname @ A_159 )
        = ( some_pname @ A_158 ) )
    <=> ( A_159 = A_158 ) ) )).

thf(fact_499_option_Oinject,axiom,(
    ! [A_159: hoare_1708887482_state,A_158: hoare_1708887482_state] :
      ( ( ( some_H1974565227_state @ A_159 )
        = ( some_H1974565227_state @ A_158 ) )
    <=> ( A_159 = A_158 ) ) )).

thf(fact_500_option_Oinject,axiom,(
    ! [A_159: com,A_158: com] :
      ( ( ( some_com @ A_159 )
        = ( some_com @ A_158 ) )
    <=> ( A_159 = A_158 ) ) )).

thf(fact_501_constant,axiom,(
    ! [G_26: hoare_1708887482_state > $o,P_29: state > state > $o,C_46: com,Q_20: state > state > $o,C_45: $o] :
      ( ( C_45
       => ( hoare_90032982_state @ G_26 @ ( insert528405184_state @ ( hoare_858012674_state @ P_29 @ C_46 @ Q_20 ) @ bot_bo19817387tate_o ) ) )
     => ( hoare_90032982_state @ G_26
        @ ( insert528405184_state
          @ ( hoare_858012674_state
            @ ^ [Z_11: state,S_2: state] :
                ( (&) @ ( P_29 @ Z_11 @ S_2 ) @ C_45 )
            @ C_46
            @ Q_20 )
          @ bot_bo19817387tate_o ) ) ) )).

thf(fact_502_Body1,axiom,(
    ! [Pn_2: pname,G_25: hoare_1708887482_state > $o,P_28: pname > state > state > $o,Q_19: pname > state > state > $o,Procs_1: pname > $o] :
      ( ( hoare_90032982_state
        @ ( semila1122118281tate_o @ G_25
          @ ( image_1116629049_state
            @ ^ [P_27: pname] :
                ( hoare_858012674_state @ ( P_28 @ P_27 ) @ ( body_1 @ P_27 ) @ ( Q_19 @ P_27 ) )
            @ Procs_1 ) )
        @ ( image_1116629049_state
          @ ^ [P_27: pname] :
              ( hoare_858012674_state @ ( P_28 @ P_27 ) @ ( the_com @ ( body @ P_27 ) ) @ ( Q_19 @ P_27 ) )
          @ Procs_1 ) )
     => ( ( member_pname @ Pn_2 @ Procs_1 )
       => ( hoare_90032982_state @ G_25 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_28 @ Pn_2 ) @ ( body_1 @ Pn_2 ) @ ( Q_19 @ Pn_2 ) ) @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_503_le__bot,axiom,(
    ! [A_157: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_157 @ bot_bot_pname_o )
     => ( A_157 = bot_bot_pname_o ) ) )).

thf(fact_504_le__bot,axiom,(
    ! [A_157: com > $o] :
      ( ( ord_less_eq_com_o @ A_157 @ bot_bot_com_o )
     => ( A_157 = bot_bot_com_o ) ) )).

thf(fact_505_le__bot,axiom,(
    ! [A_157: $o] :
      ( ( ord_less_eq_o @ A_157 @ bot_bot_o )
     => ( A_157
      <=> bot_bot_o ) ) )).

thf(fact_506_le__bot,axiom,(
    ! [A_157: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_157 @ bot_bo19817387tate_o )
     => ( A_157 = bot_bo19817387tate_o ) ) )).

thf(fact_507_bot__unique,axiom,(
    ! [A_156: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_156 @ bot_bot_pname_o )
    <=> ( A_156 = bot_bot_pname_o ) ) )).

thf(fact_508_bot__unique,axiom,(
    ! [A_156: com > $o] :
      ( ( ord_less_eq_com_o @ A_156 @ bot_bot_com_o )
    <=> ( A_156 = bot_bot_com_o ) ) )).

thf(fact_509_bot__unique,axiom,(
    ! [A_156: $o] :
      ( ( ord_less_eq_o @ A_156 @ bot_bot_o )
    <=> ( A_156
      <=> bot_bot_o ) ) )).

thf(fact_510_bot__unique,axiom,(
    ! [A_156: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_156 @ bot_bo19817387tate_o )
    <=> ( A_156 = bot_bo19817387tate_o ) ) )).

thf(fact_511_bot__least,axiom,(
    ! [A_155: pname > $o] :
      ( ord_less_eq_pname_o @ bot_bot_pname_o @ A_155 ) )).

thf(fact_512_bot__least,axiom,(
    ! [A_155: com > $o] :
      ( ord_less_eq_com_o @ bot_bot_com_o @ A_155 ) )).

thf(fact_513_bot__least,axiom,(
    ! [A_155: $o] :
      ( ord_less_eq_o @ bot_bot_o @ A_155 ) )).

thf(fact_514_bot__least,axiom,(
    ! [A_155: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ bot_bo19817387tate_o @ A_155 ) )).

thf(fact_515_le__funE,axiom,(
    ! [X_92: pname,F_65: pname > $o,G_24: pname > $o] :
      ( ( ord_less_eq_pname_o @ F_65 @ G_24 )
     => ( ord_less_eq_o @ ( F_65 @ X_92 ) @ ( G_24 @ X_92 ) ) ) )).

thf(fact_516_le__funE,axiom,(
    ! [X_92: hoare_1708887482_state,F_65: hoare_1708887482_state > $o,G_24: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ F_65 @ G_24 )
     => ( ord_less_eq_o @ ( F_65 @ X_92 ) @ ( G_24 @ X_92 ) ) ) )).

thf(fact_517_le__funD,axiom,(
    ! [X_91: pname,F_64: pname > $o,G_23: pname > $o] :
      ( ( ord_less_eq_pname_o @ F_64 @ G_23 )
     => ( ord_less_eq_o @ ( F_64 @ X_91 ) @ ( G_23 @ X_91 ) ) ) )).

thf(fact_518_le__funD,axiom,(
    ! [X_91: hoare_1708887482_state,F_64: hoare_1708887482_state > $o,G_23: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ F_64 @ G_23 )
     => ( ord_less_eq_o @ ( F_64 @ X_91 ) @ ( G_23 @ X_91 ) ) ) )).

thf(fact_519_le__fun__def,axiom,(
    ! [F_63: pname > $o,G_22: pname > $o] :
      ( ( ord_less_eq_pname_o @ F_63 @ G_22 )
    <=> ! [X_3: pname] :
          ( ord_less_eq_o @ ( F_63 @ X_3 ) @ ( G_22 @ X_3 ) ) ) )).

thf(fact_520_le__fun__def,axiom,(
    ! [F_63: hoare_1708887482_state > $o,G_22: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ F_63 @ G_22 )
    <=> ! [X_3: hoare_1708887482_state] :
          ( ord_less_eq_o @ ( F_63 @ X_3 ) @ ( G_22 @ X_3 ) ) ) )).

thf(fact_521_bot__apply,axiom,(
    ! [X_90: pname] :
      ( ( bot_bot_pname_o @ X_90 )
    <=> bot_bot_o ) )).

thf(fact_522_bot__apply,axiom,(
    ! [X_90: com] :
      ( ( bot_bot_com_o @ X_90 )
    <=> bot_bot_o ) )).

thf(fact_523_bot__apply,axiom,(
    ! [X_90: hoare_1708887482_state] :
      ( ( bot_bo19817387tate_o @ X_90 )
    <=> bot_bot_o ) )).

thf(fact_524_bot__fun__def,axiom,(
    ! [X_3: pname] :
      ( ( bot_bot_pname_o @ X_3 )
    <=> bot_bot_o ) )).

thf(fact_525_bot__fun__def,axiom,(
    ! [X_3: com] :
      ( ( bot_bot_com_o @ X_3 )
    <=> bot_bot_o ) )).

thf(fact_526_bot__fun__def,axiom,(
    ! [X_3: hoare_1708887482_state] :
      ( ( bot_bo19817387tate_o @ X_3 )
    <=> bot_bot_o ) )).

thf(fact_527_finite__pointwise,axiom,(
    ! [P_26: ( pname > $o ) > state > state > $o,Q_18: ( pname > $o ) > state > state > $o,G_21: hoare_1708887482_state > $o,P_25: ( pname > $o ) > state > state > $o,C0_1: ( pname > $o ) > com,Q_17: ( pname > $o ) > state > state > $o,U_1: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ U_1 )
     => ( ! [P_27: pname > $o] :
            ( ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) ) @ bot_bo19817387tate_o ) )
           => ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) ) @ bot_bo19817387tate_o ) ) )
       => ( ( hoare_90032982_state @ G_21
            @ ( image_1922967206_state
              @ ^ [P_27: pname > $o] :
                  ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) )
              @ U_1 ) )
         => ( hoare_90032982_state @ G_21
            @ ( image_1922967206_state
              @ ^ [P_27: pname > $o] :
                  ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) )
              @ U_1 ) ) ) ) ) )).

thf(fact_528_finite__pointwise,axiom,(
    ! [P_26: ( hoare_1708887482_state > $o ) > state > state > $o,Q_18: ( hoare_1708887482_state > $o ) > state > state > $o,G_21: hoare_1708887482_state > $o,P_25: ( hoare_1708887482_state > $o ) > state > state > $o,C0_1: ( hoare_1708887482_state > $o ) > com,Q_17: ( hoare_1708887482_state > $o ) > state > state > $o,U_1: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ U_1 )
     => ( ! [P_27: hoare_1708887482_state > $o] :
            ( ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) ) @ bot_bo19817387tate_o ) )
           => ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) ) @ bot_bo19817387tate_o ) ) )
       => ( ( hoare_90032982_state @ G_21
            @ ( image_27005066_state
              @ ^ [P_27: hoare_1708887482_state > $o] :
                  ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) )
              @ U_1 ) )
         => ( hoare_90032982_state @ G_21
            @ ( image_27005066_state
              @ ^ [P_27: hoare_1708887482_state > $o] :
                  ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) )
              @ U_1 ) ) ) ) ) )).

thf(fact_529_finite__pointwise,axiom,(
    ! [P_26: pname > state > state > $o,Q_18: pname > state > state > $o,G_21: hoare_1708887482_state > $o,P_25: pname > state > state > $o,C0_1: pname > com,Q_17: pname > state > state > $o,U_1: pname > $o] :
      ( ( finite_finite_pname @ U_1 )
     => ( ! [P_27: pname] :
            ( ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) ) @ bot_bo19817387tate_o ) )
           => ( hoare_90032982_state @ G_21 @ ( insert528405184_state @ ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) ) @ bot_bo19817387tate_o ) ) )
       => ( ( hoare_90032982_state @ G_21
            @ ( image_1116629049_state
              @ ^ [P_27: pname] :
                  ( hoare_858012674_state @ ( P_25 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_17 @ P_27 ) )
              @ U_1 ) )
         => ( hoare_90032982_state @ G_21
            @ ( image_1116629049_state
              @ ^ [P_27: pname] :
                  ( hoare_858012674_state @ ( P_26 @ P_27 ) @ ( C0_1 @ P_27 ) @ ( Q_18 @ P_27 ) )
              @ U_1 ) ) ) ) ) )).

thf(fact_530_escape,axiom,(
    ! [G_20: hoare_1708887482_state > $o,C_44: com,Q_16: state > state > $o,P_24: state > state > $o] :
      ( ! [Z_11: state,S_2: state] :
          ( ( P_24 @ Z_11 @ S_2 )
         => ( hoare_90032982_state @ G_20
            @ ( insert528405184_state
              @ ( hoare_858012674_state
                @ ^ [Za: state,S_3: state] : ( S_3 = S_2 )
                @ C_44
                @ ^ [Z_12: state] :
                    ( Q_16 @ Z_11 ) )
              @ bot_bo19817387tate_o ) ) )
     => ( hoare_90032982_state @ G_20 @ ( insert528405184_state @ ( hoare_858012674_state @ P_24 @ C_44 @ Q_16 ) @ bot_bo19817387tate_o ) ) ) )).

thf(fact_531_Body__sound__lemma,axiom,(
    ! [G_19: hoare_1708887482_state > $o,P_23: pname > state > state > $o,Q_15: pname > state > state > $o,Procs: pname > $o] :
      ( ( hoare_496444244_state
        @ ( semila1122118281tate_o @ G_19
          @ ( image_1116629049_state
            @ ^ [Pn: pname] :
                ( hoare_858012674_state @ ( P_23 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_15 @ Pn ) )
            @ Procs ) )
        @ ( image_1116629049_state
          @ ^ [Pn: pname] :
              ( hoare_858012674_state @ ( P_23 @ Pn ) @ ( the_com @ ( body @ Pn ) ) @ ( Q_15 @ Pn ) )
          @ Procs ) )
     => ( hoare_496444244_state @ G_19
        @ ( image_1116629049_state
          @ ^ [Pn: pname] :
              ( hoare_858012674_state @ ( P_23 @ Pn ) @ ( body_1 @ Pn ) @ ( Q_15 @ Pn ) )
          @ Procs ) ) ) )).

thf(fact_532_conseq1,axiom,(
    ! [P_22: state > state > $o,G_18: hoare_1708887482_state > $o,P_21: state > state > $o,C_43: com,Q_14: state > state > $o] :
      ( ( hoare_90032982_state @ G_18 @ ( insert528405184_state @ ( hoare_858012674_state @ P_21 @ C_43 @ Q_14 ) @ bot_bo19817387tate_o ) )
     => ( ! [Z_11: state,S_2: state] :
            ( ( P_22 @ Z_11 @ S_2 )
           => ( P_21 @ Z_11 @ S_2 ) )
       => ( hoare_90032982_state @ G_18 @ ( insert528405184_state @ ( hoare_858012674_state @ P_22 @ C_43 @ Q_14 ) @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_533_conseq2,axiom,(
    ! [Q_13: state > state > $o,G_17: hoare_1708887482_state > $o,P_20: state > state > $o,C_42: com,Q_12: state > state > $o] :
      ( ( hoare_90032982_state @ G_17 @ ( insert528405184_state @ ( hoare_858012674_state @ P_20 @ C_42 @ Q_12 ) @ bot_bo19817387tate_o ) )
     => ( ! [Z_11: state,S_2: state] :
            ( ( Q_12 @ Z_11 @ S_2 )
           => ( Q_13 @ Z_11 @ S_2 ) )
       => ( hoare_90032982_state @ G_17 @ ( insert528405184_state @ ( hoare_858012674_state @ P_20 @ C_42 @ Q_13 ) @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_534_MGF__complete,axiom,(
    ! [P: state > state > $o,Q_11: state > state > $o,C_34: com] :
      ( ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) )
     => ( ( hoare_496444244_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_858012674_state @ P @ C_34 @ Q_11 ) @ bot_bo19817387tate_o ) )
       => ( hoare_90032982_state @ bot_bo19817387tate_o @ ( insert528405184_state @ ( hoare_858012674_state @ P @ C_34 @ Q_11 ) @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_535_sup1E,axiom,(
    ! [A_154: pname > $o,B_100: pname > $o,X_89: pname] :
      ( ( semila1780557381name_o @ A_154 @ B_100 @ X_89 )
     => ( ~ ( A_154 @ X_89 )
       => ( B_100 @ X_89 ) ) ) )).

thf(fact_536_sup1E,axiom,(
    ! [A_154: hoare_1708887482_state > $o,B_100: hoare_1708887482_state > $o,X_89: hoare_1708887482_state] :
      ( ( semila1122118281tate_o @ A_154 @ B_100 @ X_89 )
     => ( ~ ( A_154 @ X_89 )
       => ( B_100 @ X_89 ) ) ) )).

thf(fact_537_sup1CI,axiom,(
    ! [A_153: pname > $o,B_99: pname > $o,X_88: pname] :
      ( ( ~ ( B_99 @ X_88 )
       => ( A_153 @ X_88 ) )
     => ( semila1780557381name_o @ A_153 @ B_99 @ X_88 ) ) )).

thf(fact_538_sup1CI,axiom,(
    ! [A_153: hoare_1708887482_state > $o,B_99: hoare_1708887482_state > $o,X_88: hoare_1708887482_state] :
      ( ( ~ ( B_99 @ X_88 )
       => ( A_153 @ X_88 ) )
     => ( semila1122118281tate_o @ A_153 @ B_99 @ X_88 ) ) )).

thf(fact_539_conseq12,axiom,(
    ! [Q_10: state > state > $o,P_19: state > state > $o,G_16: hoare_1708887482_state > $o,P_18: state > state > $o,C_41: com,Q_9: state > state > $o] :
      ( ( hoare_90032982_state @ G_16 @ ( insert528405184_state @ ( hoare_858012674_state @ P_18 @ C_41 @ Q_9 ) @ bot_bo19817387tate_o ) )
     => ( ! [Z_11: state,S_2: state] :
            ( ( P_19 @ Z_11 @ S_2 )
           => ! [S_3: state] :
                ( ! [Z_12: state] :
                    ( ( P_18 @ Z_12 @ S_2 )
                   => ( Q_9 @ Z_12 @ S_3 ) )
               => ( Q_10 @ Z_11 @ S_3 ) ) )
       => ( hoare_90032982_state @ G_16 @ ( insert528405184_state @ ( hoare_858012674_state @ P_19 @ C_41 @ Q_10 ) @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_540_hoare__sound,axiom,(
    ! [G_15: hoare_1708887482_state > $o,Ts: hoare_1708887482_state > $o] :
      ( ( hoare_90032982_state @ G_15 @ Ts )
     => ( hoare_496444244_state @ G_15 @ Ts ) ) )).

thf(fact_541_bot__empty__eq,axiom,(
    ! [X_3: com] :
      ( ( bot_bot_com_o @ X_3 )
    <=> ( member_com @ X_3 @ bot_bot_com_o ) ) )).

thf(fact_542_bot__empty__eq,axiom,(
    ! [X_3: hoare_1708887482_state] :
      ( ( bot_bo19817387tate_o @ X_3 )
    <=> ( member451959335_state @ X_3 @ bot_bo19817387tate_o ) ) )).

thf(fact_543_bot__empty__eq,axiom,(
    ! [X_3: pname] :
      ( ( bot_bot_pname_o @ X_3 )
    <=> ( member_pname @ X_3 @ bot_bot_pname_o ) ) )).

thf(fact_544_rev__predicate1D,axiom,(
    ! [Q_8: pname > $o,P_17: pname > $o,X_87: pname] :
      ( ( P_17 @ X_87 )
     => ( ( ord_less_eq_pname_o @ P_17 @ Q_8 )
       => ( Q_8 @ X_87 ) ) ) )).

thf(fact_545_rev__predicate1D,axiom,(
    ! [Q_8: hoare_1708887482_state > $o,P_17: hoare_1708887482_state > $o,X_87: hoare_1708887482_state] :
      ( ( P_17 @ X_87 )
     => ( ( ord_le777019615tate_o @ P_17 @ Q_8 )
       => ( Q_8 @ X_87 ) ) ) )).

thf(fact_546_predicate1D,axiom,(
    ! [X_86: pname,P_16: pname > $o,Q_7: pname > $o] :
      ( ( ord_less_eq_pname_o @ P_16 @ Q_7 )
     => ( ( P_16 @ X_86 )
       => ( Q_7 @ X_86 ) ) ) )).

thf(fact_547_predicate1D,axiom,(
    ! [X_86: hoare_1708887482_state,P_16: hoare_1708887482_state > $o,Q_7: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ P_16 @ Q_7 )
     => ( ( P_16 @ X_86 )
       => ( Q_7 @ X_86 ) ) ) )).

thf(fact_548_sup1I2,axiom,(
    ! [A_152: pname > $o,B_98: pname > $o,X_85: pname] :
      ( ( B_98 @ X_85 )
     => ( semila1780557381name_o @ A_152 @ B_98 @ X_85 ) ) )).

thf(fact_549_sup1I2,axiom,(
    ! [A_152: hoare_1708887482_state > $o,B_98: hoare_1708887482_state > $o,X_85: hoare_1708887482_state] :
      ( ( B_98 @ X_85 )
     => ( semila1122118281tate_o @ A_152 @ B_98 @ X_85 ) ) )).

thf(fact_550_sup1I1,axiom,(
    ! [B_97: pname > $o,A_151: pname > $o,X_84: pname] :
      ( ( A_151 @ X_84 )
     => ( semila1780557381name_o @ A_151 @ B_97 @ X_84 ) ) )).

thf(fact_551_sup1I1,axiom,(
    ! [B_97: hoare_1708887482_state > $o,A_151: hoare_1708887482_state > $o,X_84: hoare_1708887482_state] :
      ( ( A_151 @ X_84 )
     => ( semila1122118281tate_o @ A_151 @ B_97 @ X_84 ) ) )).

thf(fact_552_pred__subset__eq,axiom,(
    ! [R_3: com > $o,S_6: com > $o] :
      ( ( ord_less_eq_com_o
        @ ^ [X_3: com] :
            ( member_com @ X_3 @ R_3 )
        @ ^ [X_3: com] :
            ( member_com @ X_3 @ S_6 ) )
    <=> ( ord_less_eq_com_o @ R_3 @ S_6 ) ) )).

thf(fact_553_pred__subset__eq,axiom,(
    ! [R_3: hoare_1708887482_state > $o,S_6: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o
        @ ^ [X_3: hoare_1708887482_state] :
            ( member451959335_state @ X_3 @ R_3 )
        @ ^ [X_3: hoare_1708887482_state] :
            ( member451959335_state @ X_3 @ S_6 ) )
    <=> ( ord_le777019615tate_o @ R_3 @ S_6 ) ) )).

thf(fact_554_pred__subset__eq,axiom,(
    ! [R_3: pname > $o,S_6: pname > $o] :
      ( ( ord_less_eq_pname_o
        @ ^ [X_3: pname] :
            ( member_pname @ X_3 @ R_3 )
        @ ^ [X_3: pname] :
            ( member_pname @ X_3 @ S_6 ) )
    <=> ( ord_less_eq_pname_o @ R_3 @ S_6 ) ) )).

thf(fact_555_sup__Un__eq,axiom,(
    ! [R_2: com > $o,S_5: com > $o,X_3: com] :
      ( ( semila1562558655_com_o
        @ ^ [Y_4: com] :
            ( member_com @ Y_4 @ R_2 )
        @ ^ [Y_4: com] :
            ( member_com @ Y_4 @ S_5 )
        @ X_3 )
    <=> ( member_com @ X_3 @ ( semila1562558655_com_o @ R_2 @ S_5 ) ) ) )).

thf(fact_556_sup__Un__eq,axiom,(
    ! [R_2: hoare_1708887482_state > $o,S_5: hoare_1708887482_state > $o,X_3: hoare_1708887482_state] :
      ( ( semila1122118281tate_o
        @ ^ [Y_4: hoare_1708887482_state] :
            ( member451959335_state @ Y_4 @ R_2 )
        @ ^ [Y_4: hoare_1708887482_state] :
            ( member451959335_state @ Y_4 @ S_5 )
        @ X_3 )
    <=> ( member451959335_state @ X_3 @ ( semila1122118281tate_o @ R_2 @ S_5 ) ) ) )).

thf(fact_557_sup__Un__eq,axiom,(
    ! [R_2: pname > $o,S_5: pname > $o,X_3: pname] :
      ( ( semila1780557381name_o
        @ ^ [Y_4: pname] :
            ( member_pname @ Y_4 @ R_2 )
        @ ^ [Y_4: pname] :
            ( member_pname @ Y_4 @ S_5 )
        @ X_3 )
    <=> ( member_pname @ X_3 @ ( semila1780557381name_o @ R_2 @ S_5 ) ) ) )).

thf(fact_558_le__funI,axiom,(
    ! [F_62: pname > $o,G_14: pname > $o] :
      ( ! [X_3: pname] :
          ( ord_less_eq_o @ ( F_62 @ X_3 ) @ ( G_14 @ X_3 ) )
     => ( ord_less_eq_pname_o @ F_62 @ G_14 ) ) )).

thf(fact_559_le__funI,axiom,(
    ! [F_62: hoare_1708887482_state > $o,G_14: hoare_1708887482_state > $o] :
      ( ! [X_3: hoare_1708887482_state] :
          ( ord_less_eq_o @ ( F_62 @ X_3 ) @ ( G_14 @ X_3 ) )
     => ( ord_le777019615tate_o @ F_62 @ G_14 ) ) )).

thf(fact_560_Option_Oset_Osimps_I2_J,axiom,(
    ! [X_83: pname] :
      ( ( set_pname @ ( some_pname @ X_83 ) )
      = ( insert_pname @ X_83 @ bot_bot_pname_o ) ) )).

thf(fact_561_Option_Oset_Osimps_I2_J,axiom,(
    ! [X_83: com] :
      ( ( set_com @ ( some_com @ X_83 ) )
      = ( insert_com @ X_83 @ bot_bot_com_o ) ) )).

thf(fact_562_Option_Oset_Osimps_I2_J,axiom,(
    ! [X_83: hoare_1708887482_state] :
      ( ( set_Ho525251890_state @ ( some_H1974565227_state @ X_83 ) )
      = ( insert528405184_state @ X_83 @ bot_bo19817387tate_o ) ) )).

thf(fact_563_sup__apply,axiom,(
    ! [F_61: pname > $o,G_13: pname > $o,X_82: pname] :
      ( ( semila1780557381name_o @ F_61 @ G_13 @ X_82 )
    <=> ( semila10642723_sup_o @ ( F_61 @ X_82 ) @ ( G_13 @ X_82 ) ) ) )).

thf(fact_564_sup__apply,axiom,(
    ! [F_61: hoare_1708887482_state > $o,G_13: hoare_1708887482_state > $o,X_82: hoare_1708887482_state] :
      ( ( semila1122118281tate_o @ F_61 @ G_13 @ X_82 )
    <=> ( semila10642723_sup_o @ ( F_61 @ X_82 ) @ ( G_13 @ X_82 ) ) ) )).

thf(fact_565_sup__fun__def,axiom,(
    ! [F_60: pname > $o,G_12: pname > $o,X_3: pname] :
      ( ( semila1780557381name_o @ F_60 @ G_12 @ X_3 )
    <=> ( semila10642723_sup_o @ ( F_60 @ X_3 ) @ ( G_12 @ X_3 ) ) ) )).

thf(fact_566_sup__fun__def,axiom,(
    ! [F_60: hoare_1708887482_state > $o,G_12: hoare_1708887482_state > $o,X_3: hoare_1708887482_state] :
      ( ( semila1122118281tate_o @ F_60 @ G_12 @ X_3 )
    <=> ( semila10642723_sup_o @ ( F_60 @ X_3 ) @ ( G_12 @ X_3 ) ) ) )).

thf(fact_567_single__stateE,axiom,
    ( hoare_1160767572gleton
   => ! [T_1: state] :
        ~ ! [S_2: state] : ( S_2 = T_1 ) )).

thf(fact_568_sup__eq__bot__iff,axiom,(
    ! [X_81: pname > $o,Y_43: pname > $o] :
      ( ( ( semila1780557381name_o @ X_81 @ Y_43 )
        = bot_bot_pname_o )
    <=> ( ( X_81 = bot_bot_pname_o )
        & ( Y_43 = bot_bot_pname_o ) ) ) )).

thf(fact_569_sup__eq__bot__iff,axiom,(
    ! [X_81: com > $o,Y_43: com > $o] :
      ( ( ( semila1562558655_com_o @ X_81 @ Y_43 )
        = bot_bot_com_o )
    <=> ( ( X_81 = bot_bot_com_o )
        & ( Y_43 = bot_bot_com_o ) ) ) )).

thf(fact_570_sup__eq__bot__iff,axiom,(
    ! [X_81: $o,Y_43: $o] :
      ( ( ( semila10642723_sup_o @ X_81 @ Y_43 )
      <=> bot_bot_o )
    <=> ( ( X_81
        <=> bot_bot_o )
        & ( Y_43
        <=> bot_bot_o ) ) ) )).

thf(fact_571_sup__eq__bot__iff,axiom,(
    ! [X_81: hoare_1708887482_state > $o,Y_43: hoare_1708887482_state > $o] :
      ( ( ( semila1122118281tate_o @ X_81 @ Y_43 )
        = bot_bo19817387tate_o )
    <=> ( ( X_81 = bot_bo19817387tate_o )
        & ( Y_43 = bot_bo19817387tate_o ) ) ) )).

thf(fact_572_elem__set,axiom,(
    ! [X_80: com,Xo_1: option_com] :
      ( ( member_com @ X_80 @ ( set_com @ Xo_1 ) )
    <=> ( Xo_1
        = ( some_com @ X_80 ) ) ) )).

thf(fact_573_elem__set,axiom,(
    ! [X_80: hoare_1708887482_state,Xo_1: option1624383643_state] :
      ( ( member451959335_state @ X_80 @ ( set_Ho525251890_state @ Xo_1 ) )
    <=> ( Xo_1
        = ( some_H1974565227_state @ X_80 ) ) ) )).

thf(fact_574_elem__set,axiom,(
    ! [X_80: pname,Xo_1: option_pname] :
      ( ( member_pname @ X_80 @ ( set_pname @ Xo_1 ) )
    <=> ( Xo_1
        = ( some_pname @ X_80 ) ) ) )).

thf(fact_575_sup_Oidem,axiom,(
    ! [A_150: pname > $o] :
      ( ( semila1780557381name_o @ A_150 @ A_150 )
      = A_150 ) )).

thf(fact_576_sup_Oidem,axiom,(
    ! [A_150: $o] :
      ( ( semila10642723_sup_o @ A_150 @ A_150 )
    <=> A_150 ) )).

thf(fact_577_sup_Oidem,axiom,(
    ! [A_150: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_150 @ A_150 )
      = A_150 ) )).

thf(fact_578_sup__idem,axiom,(
    ! [X_79: pname > $o] :
      ( ( semila1780557381name_o @ X_79 @ X_79 )
      = X_79 ) )).

thf(fact_579_sup__idem,axiom,(
    ! [X_79: $o] :
      ( ( semila10642723_sup_o @ X_79 @ X_79 )
    <=> X_79 ) )).

thf(fact_580_sup__idem,axiom,(
    ! [X_79: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ X_79 @ X_79 )
      = X_79 ) )).

thf(fact_581_sup_Ocommute,axiom,(
    ! [A_149: pname > $o,B_96: pname > $o] :
      ( ( semila1780557381name_o @ A_149 @ B_96 )
      = ( semila1780557381name_o @ B_96 @ A_149 ) ) )).

thf(fact_582_sup_Ocommute,axiom,(
    ! [A_149: $o,B_96: $o] :
      ( ( semila10642723_sup_o @ A_149 @ B_96 )
    <=> ( semila10642723_sup_o @ B_96 @ A_149 ) ) )).

thf(fact_583_sup_Ocommute,axiom,(
    ! [A_149: hoare_1708887482_state > $o,B_96: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_149 @ B_96 )
      = ( semila1122118281tate_o @ B_96 @ A_149 ) ) )).

thf(fact_584_inf__sup__aci_I5_J,axiom,(
    ! [X_78: pname > $o,Y_42: pname > $o] :
      ( ( semila1780557381name_o @ X_78 @ Y_42 )
      = ( semila1780557381name_o @ Y_42 @ X_78 ) ) )).

thf(fact_585_inf__sup__aci_I5_J,axiom,(
    ! [X_78: $o,Y_42: $o] :
      ( ( semila10642723_sup_o @ X_78 @ Y_42 )
    <=> ( semila10642723_sup_o @ Y_42 @ X_78 ) ) )).

thf(fact_586_inf__sup__aci_I5_J,axiom,(
    ! [X_78: hoare_1708887482_state > $o,Y_42: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ X_78 @ Y_42 )
      = ( semila1122118281tate_o @ Y_42 @ X_78 ) ) )).

thf(fact_587_sup__commute,axiom,(
    ! [X_77: pname > $o,Y_41: pname > $o] :
      ( ( semila1780557381name_o @ X_77 @ Y_41 )
      = ( semila1780557381name_o @ Y_41 @ X_77 ) ) )).

thf(fact_588_sup__commute,axiom,(
    ! [X_77: $o,Y_41: $o] :
      ( ( semila10642723_sup_o @ X_77 @ Y_41 )
    <=> ( semila10642723_sup_o @ Y_41 @ X_77 ) ) )).

thf(fact_589_sup__commute,axiom,(
    ! [X_77: hoare_1708887482_state > $o,Y_41: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ X_77 @ Y_41 )
      = ( semila1122118281tate_o @ Y_41 @ X_77 ) ) )).

thf(fact_590_sup_Oleft__idem,axiom,(
    ! [A_148: pname > $o,B_95: pname > $o] :
      ( ( semila1780557381name_o @ A_148 @ ( semila1780557381name_o @ A_148 @ B_95 ) )
      = ( semila1780557381name_o @ A_148 @ B_95 ) ) )).

thf(fact_591_sup_Oleft__idem,axiom,(
    ! [A_148: $o,B_95: $o] :
      ( ( semila10642723_sup_o @ A_148 @ ( semila10642723_sup_o @ A_148 @ B_95 ) )
    <=> ( semila10642723_sup_o @ A_148 @ B_95 ) ) )).

thf(fact_592_sup_Oleft__idem,axiom,(
    ! [A_148: hoare_1708887482_state > $o,B_95: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_148 @ ( semila1122118281tate_o @ A_148 @ B_95 ) )
      = ( semila1122118281tate_o @ A_148 @ B_95 ) ) )).

thf(fact_593_inf__sup__aci_I8_J,axiom,(
    ! [X_76: pname > $o,Y_40: pname > $o] :
      ( ( semila1780557381name_o @ X_76 @ ( semila1780557381name_o @ X_76 @ Y_40 ) )
      = ( semila1780557381name_o @ X_76 @ Y_40 ) ) )).

thf(fact_594_inf__sup__aci_I8_J,axiom,(
    ! [X_76: $o,Y_40: $o] :
      ( ( semila10642723_sup_o @ X_76 @ ( semila10642723_sup_o @ X_76 @ Y_40 ) )
    <=> ( semila10642723_sup_o @ X_76 @ Y_40 ) ) )).

thf(fact_595_inf__sup__aci_I8_J,axiom,(
    ! [X_76: hoare_1708887482_state > $o,Y_40: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ X_76 @ ( semila1122118281tate_o @ X_76 @ Y_40 ) )
      = ( semila1122118281tate_o @ X_76 @ Y_40 ) ) )).

thf(fact_596_sup__left__idem,axiom,(
    ! [X_75: pname > $o,Y_39: pname > $o] :
      ( ( semila1780557381name_o @ X_75 @ ( semila1780557381name_o @ X_75 @ Y_39 ) )
      = ( semila1780557381name_o @ X_75 @ Y_39 ) ) )).

thf(fact_597_sup__left__idem,axiom,(
    ! [X_75: $o,Y_39: $o] :
      ( ( semila10642723_sup_o @ X_75 @ ( semila10642723_sup_o @ X_75 @ Y_39 ) )
    <=> ( semila10642723_sup_o @ X_75 @ Y_39 ) ) )).

thf(fact_598_sup__left__idem,axiom,(
    ! [X_75: hoare_1708887482_state > $o,Y_39: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ X_75 @ ( semila1122118281tate_o @ X_75 @ Y_39 ) )
      = ( semila1122118281tate_o @ X_75 @ Y_39 ) ) )).

thf(fact_599_sup_Oleft__commute,axiom,(
    ! [B_94: pname > $o,A_147: pname > $o,C_40: pname > $o] :
      ( ( semila1780557381name_o @ B_94 @ ( semila1780557381name_o @ A_147 @ C_40 ) )
      = ( semila1780557381name_o @ A_147 @ ( semila1780557381name_o @ B_94 @ C_40 ) ) ) )).

thf(fact_600_sup_Oleft__commute,axiom,(
    ! [B_94: $o,A_147: $o,C_40: $o] :
      ( ( semila10642723_sup_o @ B_94 @ ( semila10642723_sup_o @ A_147 @ C_40 ) )
    <=> ( semila10642723_sup_o @ A_147 @ ( semila10642723_sup_o @ B_94 @ C_40 ) ) ) )).

thf(fact_601_sup_Oleft__commute,axiom,(
    ! [B_94: hoare_1708887482_state > $o,A_147: hoare_1708887482_state > $o,C_40: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ B_94 @ ( semila1122118281tate_o @ A_147 @ C_40 ) )
      = ( semila1122118281tate_o @ A_147 @ ( semila1122118281tate_o @ B_94 @ C_40 ) ) ) )).

thf(fact_602_inf__sup__aci_I7_J,axiom,(
    ! [X_74: pname > $o,Y_38: pname > $o,Z_18: pname > $o] :
      ( ( semila1780557381name_o @ X_74 @ ( semila1780557381name_o @ Y_38 @ Z_18 ) )
      = ( semila1780557381name_o @ Y_38 @ ( semila1780557381name_o @ X_74 @ Z_18 ) ) ) )).

thf(fact_603_inf__sup__aci_I7_J,axiom,(
    ! [X_74: $o,Y_38: $o,Z_18: $o] :
      ( ( semila10642723_sup_o @ X_74 @ ( semila10642723_sup_o @ Y_38 @ Z_18 ) )
    <=> ( semila10642723_sup_o @ Y_38 @ ( semila10642723_sup_o @ X_74 @ Z_18 ) ) ) )).

thf(fact_604_inf__sup__aci_I7_J,axiom,(
    ! [X_74: hoare_1708887482_state > $o,Y_38: hoare_1708887482_state > $o,Z_18: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ X_74 @ ( semila1122118281tate_o @ Y_38 @ Z_18 ) )
      = ( semila1122118281tate_o @ Y_38 @ ( semila1122118281tate_o @ X_74 @ Z_18 ) ) ) )).

thf(fact_605_sup__left__commute,axiom,(
    ! [X_73: pname > $o,Y_37: pname > $o,Z_17: pname > $o] :
      ( ( semila1780557381name_o @ X_73 @ ( semila1780557381name_o @ Y_37 @ Z_17 ) )
      = ( semila1780557381name_o @ Y_37 @ ( semila1780557381name_o @ X_73 @ Z_17 ) ) ) )).

thf(fact_606_sup__left__commute,axiom,(
    ! [X_73: $o,Y_37: $o,Z_17: $o] :
      ( ( semila10642723_sup_o @ X_73 @ ( semila10642723_sup_o @ Y_37 @ Z_17 ) )
    <=> ( semila10642723_sup_o @ Y_37 @ ( semila10642723_sup_o @ X_73 @ Z_17 ) ) ) )).

thf(fact_607_sup__left__commute,axiom,(
    ! [X_73: hoare_1708887482_state > $o,Y_37: hoare_1708887482_state > $o,Z_17: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ X_73 @ ( semila1122118281tate_o @ Y_37 @ Z_17 ) )
      = ( semila1122118281tate_o @ Y_37 @ ( semila1122118281tate_o @ X_73 @ Z_17 ) ) ) )).

thf(fact_608_sup_Oassoc,axiom,(
    ! [A_146: pname > $o,B_93: pname > $o,C_39: pname > $o] :
      ( ( semila1780557381name_o @ ( semila1780557381name_o @ A_146 @ B_93 ) @ C_39 )
      = ( semila1780557381name_o @ A_146 @ ( semila1780557381name_o @ B_93 @ C_39 ) ) ) )).

thf(fact_609_sup_Oassoc,axiom,(
    ! [A_146: $o,B_93: $o,C_39: $o] :
      ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ A_146 @ B_93 ) @ C_39 )
    <=> ( semila10642723_sup_o @ A_146 @ ( semila10642723_sup_o @ B_93 @ C_39 ) ) ) )).

thf(fact_610_sup_Oassoc,axiom,(
    ! [A_146: hoare_1708887482_state > $o,B_93: hoare_1708887482_state > $o,C_39: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ A_146 @ B_93 ) @ C_39 )
      = ( semila1122118281tate_o @ A_146 @ ( semila1122118281tate_o @ B_93 @ C_39 ) ) ) )).

thf(fact_611_inf__sup__aci_I6_J,axiom,(
    ! [X_72: pname > $o,Y_36: pname > $o,Z_16: pname > $o] :
      ( ( semila1780557381name_o @ ( semila1780557381name_o @ X_72 @ Y_36 ) @ Z_16 )
      = ( semila1780557381name_o @ X_72 @ ( semila1780557381name_o @ Y_36 @ Z_16 ) ) ) )).

thf(fact_612_inf__sup__aci_I6_J,axiom,(
    ! [X_72: $o,Y_36: $o,Z_16: $o] :
      ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ X_72 @ Y_36 ) @ Z_16 )
    <=> ( semila10642723_sup_o @ X_72 @ ( semila10642723_sup_o @ Y_36 @ Z_16 ) ) ) )).

thf(fact_613_inf__sup__aci_I6_J,axiom,(
    ! [X_72: hoare_1708887482_state > $o,Y_36: hoare_1708887482_state > $o,Z_16: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ X_72 @ Y_36 ) @ Z_16 )
      = ( semila1122118281tate_o @ X_72 @ ( semila1122118281tate_o @ Y_36 @ Z_16 ) ) ) )).

thf(fact_614_sup__assoc,axiom,(
    ! [X_71: pname > $o,Y_35: pname > $o,Z_15: pname > $o] :
      ( ( semila1780557381name_o @ ( semila1780557381name_o @ X_71 @ Y_35 ) @ Z_15 )
      = ( semila1780557381name_o @ X_71 @ ( semila1780557381name_o @ Y_35 @ Z_15 ) ) ) )).

thf(fact_615_sup__assoc,axiom,(
    ! [X_71: $o,Y_35: $o,Z_15: $o] :
      ( ( semila10642723_sup_o @ ( semila10642723_sup_o @ X_71 @ Y_35 ) @ Z_15 )
    <=> ( semila10642723_sup_o @ X_71 @ ( semila10642723_sup_o @ Y_35 @ Z_15 ) ) ) )).

thf(fact_616_sup__assoc,axiom,(
    ! [X_71: hoare_1708887482_state > $o,Y_35: hoare_1708887482_state > $o,Z_15: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ X_71 @ Y_35 ) @ Z_15 )
      = ( semila1122118281tate_o @ X_71 @ ( semila1122118281tate_o @ Y_35 @ Z_15 ) ) ) )).

thf(fact_617_inf__sup__ord_I3_J,axiom,(
    ! [X_70: pname > $o,Y_34: pname > $o] :
      ( ord_less_eq_pname_o @ X_70 @ ( semila1780557381name_o @ X_70 @ Y_34 ) ) )).

thf(fact_618_inf__sup__ord_I3_J,axiom,(
    ! [X_70: $o,Y_34: $o] :
      ( ord_less_eq_o @ X_70 @ ( semila10642723_sup_o @ X_70 @ Y_34 ) ) )).

thf(fact_619_inf__sup__ord_I3_J,axiom,(
    ! [X_70: hoare_1708887482_state > $o,Y_34: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ X_70 @ ( semila1122118281tate_o @ X_70 @ Y_34 ) ) )).

thf(fact_620_sup__ge1,axiom,(
    ! [X_69: pname > $o,Y_33: pname > $o] :
      ( ord_less_eq_pname_o @ X_69 @ ( semila1780557381name_o @ X_69 @ Y_33 ) ) )).

thf(fact_621_sup__ge1,axiom,(
    ! [X_69: $o,Y_33: $o] :
      ( ord_less_eq_o @ X_69 @ ( semila10642723_sup_o @ X_69 @ Y_33 ) ) )).

thf(fact_622_sup__ge1,axiom,(
    ! [X_69: hoare_1708887482_state > $o,Y_33: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ X_69 @ ( semila1122118281tate_o @ X_69 @ Y_33 ) ) )).

thf(fact_623_inf__sup__ord_I4_J,axiom,(
    ! [Y_32: pname > $o,X_68: pname > $o] :
      ( ord_less_eq_pname_o @ Y_32 @ ( semila1780557381name_o @ X_68 @ Y_32 ) ) )).

thf(fact_624_inf__sup__ord_I4_J,axiom,(
    ! [Y_32: $o,X_68: $o] :
      ( ord_less_eq_o @ Y_32 @ ( semila10642723_sup_o @ X_68 @ Y_32 ) ) )).

thf(fact_625_inf__sup__ord_I4_J,axiom,(
    ! [Y_32: hoare_1708887482_state > $o,X_68: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ Y_32 @ ( semila1122118281tate_o @ X_68 @ Y_32 ) ) )).

thf(fact_626_sup__ge2,axiom,(
    ! [Y_31: pname > $o,X_67: pname > $o] :
      ( ord_less_eq_pname_o @ Y_31 @ ( semila1780557381name_o @ X_67 @ Y_31 ) ) )).

thf(fact_627_sup__ge2,axiom,(
    ! [Y_31: $o,X_67: $o] :
      ( ord_less_eq_o @ Y_31 @ ( semila10642723_sup_o @ X_67 @ Y_31 ) ) )).

thf(fact_628_sup__ge2,axiom,(
    ! [Y_31: hoare_1708887482_state > $o,X_67: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ Y_31 @ ( semila1122118281tate_o @ X_67 @ Y_31 ) ) )).

thf(fact_629_le__iff__sup,axiom,(
    ! [X_66: pname > $o,Y_30: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_66 @ Y_30 )
    <=> ( ( semila1780557381name_o @ X_66 @ Y_30 )
        = Y_30 ) ) )).

thf(fact_630_le__iff__sup,axiom,(
    ! [X_66: $o,Y_30: $o] :
      ( ( ord_less_eq_o @ X_66 @ Y_30 )
    <=> ( ( semila10642723_sup_o @ X_66 @ Y_30 )
      <=> Y_30 ) ) )).

thf(fact_631_le__iff__sup,axiom,(
    ! [X_66: hoare_1708887482_state > $o,Y_30: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_66 @ Y_30 )
    <=> ( ( semila1122118281tate_o @ X_66 @ Y_30 )
        = Y_30 ) ) )).

thf(fact_632_le__sup__iff,axiom,(
    ! [X_65: pname > $o,Y_29: pname > $o,Z_14: pname > $o] :
      ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_65 @ Y_29 ) @ Z_14 )
    <=> ( ( ord_less_eq_pname_o @ X_65 @ Z_14 )
        & ( ord_less_eq_pname_o @ Y_29 @ Z_14 ) ) ) )).

thf(fact_633_le__sup__iff,axiom,(
    ! [X_65: $o,Y_29: $o,Z_14: $o] :
      ( ( ord_less_eq_o @ ( semila10642723_sup_o @ X_65 @ Y_29 ) @ Z_14 )
    <=> ( ( ord_less_eq_o @ X_65 @ Z_14 )
        & ( ord_less_eq_o @ Y_29 @ Z_14 ) ) ) )).

thf(fact_634_le__sup__iff,axiom,(
    ! [X_65: hoare_1708887482_state > $o,Y_29: hoare_1708887482_state > $o,Z_14: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ ( semila1122118281tate_o @ X_65 @ Y_29 ) @ Z_14 )
    <=> ( ( ord_le777019615tate_o @ X_65 @ Z_14 )
        & ( ord_le777019615tate_o @ Y_29 @ Z_14 ) ) ) )).

thf(fact_635_le__supI1,axiom,(
    ! [B_92: pname > $o,X_64: pname > $o,A_145: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_64 @ A_145 )
     => ( ord_less_eq_pname_o @ X_64 @ ( semila1780557381name_o @ A_145 @ B_92 ) ) ) )).

thf(fact_636_le__supI1,axiom,(
    ! [B_92: $o,X_64: $o,A_145: $o] :
      ( ( ord_less_eq_o @ X_64 @ A_145 )
     => ( ord_less_eq_o @ X_64 @ ( semila10642723_sup_o @ A_145 @ B_92 ) ) ) )).

thf(fact_637_le__supI1,axiom,(
    ! [B_92: hoare_1708887482_state > $o,X_64: hoare_1708887482_state > $o,A_145: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_64 @ A_145 )
     => ( ord_le777019615tate_o @ X_64 @ ( semila1122118281tate_o @ A_145 @ B_92 ) ) ) )).

thf(fact_638_le__supI2,axiom,(
    ! [A_144: pname > $o,X_63: pname > $o,B_91: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_63 @ B_91 )
     => ( ord_less_eq_pname_o @ X_63 @ ( semila1780557381name_o @ A_144 @ B_91 ) ) ) )).

thf(fact_639_le__supI2,axiom,(
    ! [A_144: $o,X_63: $o,B_91: $o] :
      ( ( ord_less_eq_o @ X_63 @ B_91 )
     => ( ord_less_eq_o @ X_63 @ ( semila10642723_sup_o @ A_144 @ B_91 ) ) ) )).

thf(fact_640_le__supI2,axiom,(
    ! [A_144: hoare_1708887482_state > $o,X_63: hoare_1708887482_state > $o,B_91: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_63 @ B_91 )
     => ( ord_le777019615tate_o @ X_63 @ ( semila1122118281tate_o @ A_144 @ B_91 ) ) ) )).

thf(fact_641_sup__absorb2,axiom,(
    ! [X_62: pname > $o,Y_28: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_62 @ Y_28 )
     => ( ( semila1780557381name_o @ X_62 @ Y_28 )
        = Y_28 ) ) )).

thf(fact_642_sup__absorb2,axiom,(
    ! [X_62: $o,Y_28: $o] :
      ( ( ord_less_eq_o @ X_62 @ Y_28 )
     => ( ( semila10642723_sup_o @ X_62 @ Y_28 )
      <=> Y_28 ) ) )).

thf(fact_643_sup__absorb2,axiom,(
    ! [X_62: hoare_1708887482_state > $o,Y_28: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_62 @ Y_28 )
     => ( ( semila1122118281tate_o @ X_62 @ Y_28 )
        = Y_28 ) ) )).

thf(fact_644_sup__absorb1,axiom,(
    ! [Y_27: pname > $o,X_61: pname > $o] :
      ( ( ord_less_eq_pname_o @ Y_27 @ X_61 )
     => ( ( semila1780557381name_o @ X_61 @ Y_27 )
        = X_61 ) ) )).

thf(fact_645_sup__absorb1,axiom,(
    ! [Y_27: $o,X_61: $o] :
      ( ( ord_less_eq_o @ Y_27 @ X_61 )
     => ( ( semila10642723_sup_o @ X_61 @ Y_27 )
      <=> X_61 ) ) )).

thf(fact_646_sup__absorb1,axiom,(
    ! [Y_27: hoare_1708887482_state > $o,X_61: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ Y_27 @ X_61 )
     => ( ( semila1122118281tate_o @ X_61 @ Y_27 )
        = X_61 ) ) )).

thf(fact_647_le__supI,axiom,(
    ! [B_90: pname > $o,A_143: pname > $o,X_60: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_143 @ X_60 )
     => ( ( ord_less_eq_pname_o @ B_90 @ X_60 )
       => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_143 @ B_90 ) @ X_60 ) ) ) )).

thf(fact_648_le__supI,axiom,(
    ! [B_90: $o,A_143: $o,X_60: $o] :
      ( ( ord_less_eq_o @ A_143 @ X_60 )
     => ( ( ord_less_eq_o @ B_90 @ X_60 )
       => ( ord_less_eq_o @ ( semila10642723_sup_o @ A_143 @ B_90 ) @ X_60 ) ) ) )).

thf(fact_649_le__supI,axiom,(
    ! [B_90: hoare_1708887482_state > $o,A_143: hoare_1708887482_state > $o,X_60: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_143 @ X_60 )
     => ( ( ord_le777019615tate_o @ B_90 @ X_60 )
       => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_143 @ B_90 ) @ X_60 ) ) ) )).

thf(fact_650_sup__least,axiom,(
    ! [Z_13: pname > $o,Y_26: pname > $o,X_59: pname > $o] :
      ( ( ord_less_eq_pname_o @ Y_26 @ X_59 )
     => ( ( ord_less_eq_pname_o @ Z_13 @ X_59 )
       => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ Y_26 @ Z_13 ) @ X_59 ) ) ) )).

thf(fact_651_sup__least,axiom,(
    ! [Z_13: $o,Y_26: $o,X_59: $o] :
      ( ( ord_less_eq_o @ Y_26 @ X_59 )
     => ( ( ord_less_eq_o @ Z_13 @ X_59 )
       => ( ord_less_eq_o @ ( semila10642723_sup_o @ Y_26 @ Z_13 ) @ X_59 ) ) ) )).

thf(fact_652_sup__least,axiom,(
    ! [Z_13: hoare_1708887482_state > $o,Y_26: hoare_1708887482_state > $o,X_59: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ Y_26 @ X_59 )
     => ( ( ord_le777019615tate_o @ Z_13 @ X_59 )
       => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ Y_26 @ Z_13 ) @ X_59 ) ) ) )).

thf(fact_653_sup__mono,axiom,(
    ! [B_89: pname > $o,D_4: pname > $o,A_142: pname > $o,C_38: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_142 @ C_38 )
     => ( ( ord_less_eq_pname_o @ B_89 @ D_4 )
       => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_142 @ B_89 ) @ ( semila1780557381name_o @ C_38 @ D_4 ) ) ) ) )).

thf(fact_654_sup__mono,axiom,(
    ! [B_89: $o,D_4: $o,A_142: $o,C_38: $o] :
      ( ( ord_less_eq_o @ A_142 @ C_38 )
     => ( ( ord_less_eq_o @ B_89 @ D_4 )
       => ( ord_less_eq_o @ ( semila10642723_sup_o @ A_142 @ B_89 ) @ ( semila10642723_sup_o @ C_38 @ D_4 ) ) ) ) )).

thf(fact_655_sup__mono,axiom,(
    ! [B_89: hoare_1708887482_state > $o,D_4: hoare_1708887482_state > $o,A_142: hoare_1708887482_state > $o,C_38: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_142 @ C_38 )
     => ( ( ord_le777019615tate_o @ B_89 @ D_4 )
       => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_142 @ B_89 ) @ ( semila1122118281tate_o @ C_38 @ D_4 ) ) ) ) )).

thf(fact_656_le__supE,axiom,(
    ! [A_141: pname > $o,B_88: pname > $o,X_58: pname > $o] :
      ( ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_141 @ B_88 ) @ X_58 )
     => ~ ( ( ord_less_eq_pname_o @ A_141 @ X_58 )
         => ~ ( ord_less_eq_pname_o @ B_88 @ X_58 ) ) ) )).

thf(fact_657_le__supE,axiom,(
    ! [A_141: $o,B_88: $o,X_58: $o] :
      ( ( ord_less_eq_o @ ( semila10642723_sup_o @ A_141 @ B_88 ) @ X_58 )
     => ~ ( ( ord_less_eq_o @ A_141 @ X_58 )
         => ~ ( ord_less_eq_o @ B_88 @ X_58 ) ) ) )).

thf(fact_658_le__supE,axiom,(
    ! [A_141: hoare_1708887482_state > $o,B_88: hoare_1708887482_state > $o,X_58: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_141 @ B_88 ) @ X_58 )
     => ~ ( ( ord_le777019615tate_o @ A_141 @ X_58 )
         => ~ ( ord_le777019615tate_o @ B_88 @ X_58 ) ) ) )).

thf(fact_659_sup__bot__left,axiom,(
    ! [X_57: pname > $o] :
      ( ( semila1780557381name_o @ bot_bot_pname_o @ X_57 )
      = X_57 ) )).

thf(fact_660_sup__bot__left,axiom,(
    ! [X_57: com > $o] :
      ( ( semila1562558655_com_o @ bot_bot_com_o @ X_57 )
      = X_57 ) )).

thf(fact_661_sup__bot__left,axiom,(
    ! [X_57: $o] :
      ( ( semila10642723_sup_o @ bot_bot_o @ X_57 )
    <=> X_57 ) )).

thf(fact_662_sup__bot__left,axiom,(
    ! [X_57: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ bot_bo19817387tate_o @ X_57 )
      = X_57 ) )).

thf(fact_663_sup__bot__right,axiom,(
    ! [X_56: pname > $o] :
      ( ( semila1780557381name_o @ X_56 @ bot_bot_pname_o )
      = X_56 ) )).

thf(fact_664_sup__bot__right,axiom,(
    ! [X_56: com > $o] :
      ( ( semila1562558655_com_o @ X_56 @ bot_bot_com_o )
      = X_56 ) )).

thf(fact_665_sup__bot__right,axiom,(
    ! [X_56: $o] :
      ( ( semila10642723_sup_o @ X_56 @ bot_bot_o )
    <=> X_56 ) )).

thf(fact_666_sup__bot__right,axiom,(
    ! [X_56: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ X_56 @ bot_bo19817387tate_o )
      = X_56 ) )).

thf(fact_667_ospec,axiom,(
    ! [X_55: pname,P_15: pname > $o,A_140: option_pname] :
      ( ! [X_3: pname] :
          ( ( member_pname @ X_3 @ ( set_pname @ A_140 ) )
         => ( P_15 @ X_3 ) )
     => ( ( A_140
          = ( some_pname @ X_55 ) )
       => ( P_15 @ X_55 ) ) ) )).

thf(fact_668_ospec,axiom,(
    ! [X_55: hoare_1708887482_state,P_15: hoare_1708887482_state > $o,A_140: option1624383643_state] :
      ( ! [X_3: hoare_1708887482_state] :
          ( ( member451959335_state @ X_3 @ ( set_Ho525251890_state @ A_140 ) )
         => ( P_15 @ X_3 ) )
     => ( ( A_140
          = ( some_H1974565227_state @ X_55 ) )
       => ( P_15 @ X_55 ) ) ) )).

thf(fact_669_ospec,axiom,(
    ! [X_55: com,P_15: com > $o,A_140: option_com] :
      ( ! [X_3: com] :
          ( ( member_com @ X_3 @ ( set_com @ A_140 ) )
         => ( P_15 @ X_3 ) )
     => ( ( A_140
          = ( some_com @ X_55 ) )
       => ( P_15 @ X_55 ) ) ) )).

thf(fact_670_folding__one__idem_Ounion__idem,axiom,(
    ! [B_87: ( pname > $o ) > $o,A_139: ( pname > $o ) > $o,F_59: ( pname > $o ) > ( pname > $o ) > pname > $o,F_58: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite697516351name_o @ F_59 @ F_58 )
     => ( ( finite297249702name_o @ A_139 )
       => ( ( A_139 != bot_bot_pname_o_o )
         => ( ( finite297249702name_o @ B_87 )
           => ( ( B_87 != bot_bot_pname_o_o )
             => ( ( F_58 @ ( semila181081674me_o_o @ A_139 @ B_87 ) )
                = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) )).

thf(fact_671_folding__one__idem_Ounion__idem,axiom,(
    ! [B_87: ( hoare_1708887482_state > $o ) > $o,A_139: ( hoare_1708887482_state > $o ) > $o,F_59: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_58: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite621643279tate_o @ F_59 @ F_58 )
     => ( ( finite1329924456tate_o @ A_139 )
       => ( ( A_139 != bot_bo1678742418te_o_o )
         => ( ( finite1329924456tate_o @ B_87 )
           => ( ( B_87 != bot_bo1678742418te_o_o )
             => ( ( F_58 @ ( semila1853742644te_o_o @ A_139 @ B_87 ) )
                = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) )).

thf(fact_672_folding__one__idem_Ounion__idem,axiom,(
    ! [B_87: com > $o,A_139: com > $o,F_59: com > com > com,F_58: ( com > $o ) > com] :
      ( ( finite666746948em_com @ F_59 @ F_58 )
     => ( ( finite_finite_com @ A_139 )
       => ( ( A_139 != bot_bot_com_o )
         => ( ( finite_finite_com @ B_87 )
           => ( ( B_87 != bot_bot_com_o )
             => ( ( F_58 @ ( semila1562558655_com_o @ A_139 @ B_87 ) )
                = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) )).

thf(fact_673_folding__one__idem_Ounion__idem,axiom,(
    ! [B_87: hoare_1708887482_state > $o,A_139: hoare_1708887482_state > $o,F_59: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_58: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1347568576_state @ F_59 @ F_58 )
     => ( ( finite1625599783_state @ A_139 )
       => ( ( A_139 != bot_bo19817387tate_o )
         => ( ( finite1625599783_state @ B_87 )
           => ( ( B_87 != bot_bo19817387tate_o )
             => ( ( F_58 @ ( semila1122118281tate_o @ A_139 @ B_87 ) )
                = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) )).

thf(fact_674_folding__one__idem_Ounion__idem,axiom,(
    ! [B_87: pname > $o,A_139: pname > $o,F_59: pname > pname > pname,F_58: ( pname > $o ) > pname] :
      ( ( finite89670078_pname @ F_59 @ F_58 )
     => ( ( finite_finite_pname @ A_139 )
       => ( ( A_139 != bot_bot_pname_o )
         => ( ( finite_finite_pname @ B_87 )
           => ( ( B_87 != bot_bot_pname_o )
             => ( ( F_58 @ ( semila1780557381name_o @ A_139 @ B_87 ) )
                = ( F_59 @ ( F_58 @ A_139 ) @ ( F_58 @ B_87 ) ) ) ) ) ) ) ) )).

thf(fact_675_folding__one__idem_Osubset__idem,axiom,(
    ! [B_86: ( pname > $o ) > $o,A_138: ( pname > $o ) > $o,F_57: ( pname > $o ) > ( pname > $o ) > pname > $o,F_56: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite697516351name_o @ F_57 @ F_56 )
     => ( ( finite297249702name_o @ A_138 )
       => ( ( B_86 != bot_bot_pname_o_o )
         => ( ( ord_le1205211808me_o_o @ B_86 @ A_138 )
           => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
              = ( F_56 @ A_138 ) ) ) ) ) ) )).

thf(fact_676_folding__one__idem_Osubset__idem,axiom,(
    ! [B_86: ( hoare_1708887482_state > $o ) > $o,A_138: ( hoare_1708887482_state > $o ) > $o,F_57: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_56: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite621643279tate_o @ F_57 @ F_56 )
     => ( ( finite1329924456tate_o @ A_138 )
       => ( ( B_86 != bot_bo1678742418te_o_o )
         => ( ( ord_le1728773982te_o_o @ B_86 @ A_138 )
           => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
              = ( F_56 @ A_138 ) ) ) ) ) ) )).

thf(fact_677_folding__one__idem_Osubset__idem,axiom,(
    ! [B_86: com > $o,A_138: com > $o,F_57: com > com > com,F_56: ( com > $o ) > com] :
      ( ( finite666746948em_com @ F_57 @ F_56 )
     => ( ( finite_finite_com @ A_138 )
       => ( ( B_86 != bot_bot_com_o )
         => ( ( ord_less_eq_com_o @ B_86 @ A_138 )
           => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
              = ( F_56 @ A_138 ) ) ) ) ) ) )).

thf(fact_678_folding__one__idem_Osubset__idem,axiom,(
    ! [B_86: hoare_1708887482_state > $o,A_138: hoare_1708887482_state > $o,F_57: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_56: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1347568576_state @ F_57 @ F_56 )
     => ( ( finite1625599783_state @ A_138 )
       => ( ( B_86 != bot_bo19817387tate_o )
         => ( ( ord_le777019615tate_o @ B_86 @ A_138 )
           => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
              = ( F_56 @ A_138 ) ) ) ) ) ) )).

thf(fact_679_folding__one__idem_Osubset__idem,axiom,(
    ! [B_86: pname > $o,A_138: pname > $o,F_57: pname > pname > pname,F_56: ( pname > $o ) > pname] :
      ( ( finite89670078_pname @ F_57 @ F_56 )
     => ( ( finite_finite_pname @ A_138 )
       => ( ( B_86 != bot_bot_pname_o )
         => ( ( ord_less_eq_pname_o @ B_86 @ A_138 )
           => ( ( F_57 @ ( F_56 @ B_86 ) @ ( F_56 @ A_138 ) )
              = ( F_56 @ A_138 ) ) ) ) ) ) )).

thf(fact_680_hoare__derivs_OSkip,axiom,(
    ! [G_11: hoare_1708887482_state > $o,P_14: state > state > $o] :
      ( hoare_90032982_state @ G_11 @ ( insert528405184_state @ ( hoare_858012674_state @ P_14 @ skip @ P_14 ) @ bot_bo19817387tate_o ) ) )).

thf(fact_681_folding__one__idem_Oinsert__idem,axiom,(
    ! [X_54: com,A_137: com > $o,F_55: com > com > com,F_54: ( com > $o ) > com] :
      ( ( finite666746948em_com @ F_55 @ F_54 )
     => ( ( finite_finite_com @ A_137 )
       => ( ( A_137 != bot_bot_com_o )
         => ( ( F_54 @ ( insert_com @ X_54 @ A_137 ) )
            = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) )).

thf(fact_682_folding__one__idem_Oinsert__idem,axiom,(
    ! [X_54: pname > $o,A_137: ( pname > $o ) > $o,F_55: ( pname > $o ) > ( pname > $o ) > pname > $o,F_54: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite697516351name_o @ F_55 @ F_54 )
     => ( ( finite297249702name_o @ A_137 )
       => ( ( A_137 != bot_bot_pname_o_o )
         => ( ( F_54 @ ( insert_pname_o @ X_54 @ A_137 ) )
            = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) )).

thf(fact_683_folding__one__idem_Oinsert__idem,axiom,(
    ! [X_54: hoare_1708887482_state > $o,A_137: ( hoare_1708887482_state > $o ) > $o,F_55: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_54: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite621643279tate_o @ F_55 @ F_54 )
     => ( ( finite1329924456tate_o @ A_137 )
       => ( ( A_137 != bot_bo1678742418te_o_o )
         => ( ( F_54 @ ( insert949073679tate_o @ X_54 @ A_137 ) )
            = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) )).

thf(fact_684_folding__one__idem_Oinsert__idem,axiom,(
    ! [X_54: pname,A_137: pname > $o,F_55: pname > pname > pname,F_54: ( pname > $o ) > pname] :
      ( ( finite89670078_pname @ F_55 @ F_54 )
     => ( ( finite_finite_pname @ A_137 )
       => ( ( A_137 != bot_bot_pname_o )
         => ( ( F_54 @ ( insert_pname @ X_54 @ A_137 ) )
            = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) )).

thf(fact_685_folding__one__idem_Oinsert__idem,axiom,(
    ! [X_54: hoare_1708887482_state,A_137: hoare_1708887482_state > $o,F_55: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_54: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1347568576_state @ F_55 @ F_54 )
     => ( ( finite1625599783_state @ A_137 )
       => ( ( A_137 != bot_bo19817387tate_o )
         => ( ( F_54 @ ( insert528405184_state @ X_54 @ A_137 ) )
            = ( F_55 @ X_54 @ ( F_54 @ A_137 ) ) ) ) ) ) )).

thf(fact_686_finite__ne__induct,axiom,(
    ! [P_13: ( com > $o ) > $o,F_52: com > $o] :
      ( ( finite_finite_com @ F_52 )
     => ( ( F_52 != bot_bot_com_o )
       => ( ! [X_3: com] :
              ( P_13 @ ( insert_com @ X_3 @ bot_bot_com_o ) )
         => ( ! [X_3: com,F_53: com > $o] :
                ( ( finite_finite_com @ F_53 )
               => ( ( F_53 != bot_bot_com_o )
                 => ( ~ ( member_com @ X_3 @ F_53 )
                   => ( ( P_13 @ F_53 )
                     => ( P_13 @ ( insert_com @ X_3 @ F_53 ) ) ) ) ) )
           => ( P_13 @ F_52 ) ) ) ) ) )).

thf(fact_687_finite__ne__induct,axiom,(
    ! [P_13: ( ( pname > $o ) > $o ) > $o,F_52: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ F_52 )
     => ( ( F_52 != bot_bot_pname_o_o )
       => ( ! [X_3: pname > $o] :
              ( P_13 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
         => ( ! [X_3: pname > $o,F_53: ( pname > $o ) > $o] :
                ( ( finite297249702name_o @ F_53 )
               => ( ( F_53 != bot_bot_pname_o_o )
                 => ( ~ ( member_pname_o @ X_3 @ F_53 )
                   => ( ( P_13 @ F_53 )
                     => ( P_13 @ ( insert_pname_o @ X_3 @ F_53 ) ) ) ) ) )
           => ( P_13 @ F_52 ) ) ) ) ) )).

thf(fact_688_finite__ne__induct,axiom,(
    ! [P_13: ( ( hoare_1708887482_state > $o ) > $o ) > $o,F_52: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ F_52 )
     => ( ( F_52 != bot_bo1678742418te_o_o )
       => ( ! [X_3: hoare_1708887482_state > $o] :
              ( P_13 @ ( insert949073679tate_o @ X_3 @ bot_bo1678742418te_o_o ) )
         => ( ! [X_3: hoare_1708887482_state > $o,F_53: ( hoare_1708887482_state > $o ) > $o] :
                ( ( finite1329924456tate_o @ F_53 )
               => ( ( F_53 != bot_bo1678742418te_o_o )
                 => ( ~ ( member814030440tate_o @ X_3 @ F_53 )
                   => ( ( P_13 @ F_53 )
                     => ( P_13 @ ( insert949073679tate_o @ X_3 @ F_53 ) ) ) ) ) )
           => ( P_13 @ F_52 ) ) ) ) ) )).

thf(fact_689_finite__ne__induct,axiom,(
    ! [P_13: ( pname > $o ) > $o,F_52: pname > $o] :
      ( ( finite_finite_pname @ F_52 )
     => ( ( F_52 != bot_bot_pname_o )
       => ( ! [X_3: pname] :
              ( P_13 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
         => ( ! [X_3: pname,F_53: pname > $o] :
                ( ( finite_finite_pname @ F_53 )
               => ( ( F_53 != bot_bot_pname_o )
                 => ( ~ ( member_pname @ X_3 @ F_53 )
                   => ( ( P_13 @ F_53 )
                     => ( P_13 @ ( insert_pname @ X_3 @ F_53 ) ) ) ) ) )
           => ( P_13 @ F_52 ) ) ) ) ) )).

thf(fact_690_finite__ne__induct,axiom,(
    ! [P_13: ( hoare_1708887482_state > $o ) > $o,F_52: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ F_52 )
     => ( ( F_52 != bot_bo19817387tate_o )
       => ( ! [X_3: hoare_1708887482_state] :
              ( P_13 @ ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) )
         => ( ! [X_3: hoare_1708887482_state,F_53: hoare_1708887482_state > $o] :
                ( ( finite1625599783_state @ F_53 )
               => ( ( F_53 != bot_bo19817387tate_o )
                 => ( ~ ( member451959335_state @ X_3 @ F_53 )
                   => ( ( P_13 @ F_53 )
                     => ( P_13 @ ( insert528405184_state @ X_3 @ F_53 ) ) ) ) ) )
           => ( P_13 @ F_52 ) ) ) ) ) )).

thf(fact_691_LoopF,axiom,(
    ! [G_10: hoare_1708887482_state > $o,P_12: state > state > $o,B_85: state > $o,C_37: com] :
      ( hoare_90032982_state @ G_10
      @ ( insert528405184_state
        @ ( hoare_858012674_state
          @ ^ [Z_11: state,S_2: state] :
              ( (&) @ ( P_12 @ Z_11 @ S_2 ) @ ( (~) @ ( B_85 @ S_2 ) ) )
          @ ( while @ B_85 @ C_37 )
          @ P_12 )
        @ bot_bo19817387tate_o ) ) )).

thf(fact_692_Comp,axiom,(
    ! [D_3: com,R_1: state > state > $o,G_9: hoare_1708887482_state > $o,P_11: state > state > $o,C_36: com,Q_6: state > state > $o] :
      ( ( hoare_90032982_state @ G_9 @ ( insert528405184_state @ ( hoare_858012674_state @ P_11 @ C_36 @ Q_6 ) @ bot_bo19817387tate_o ) )
     => ( ( hoare_90032982_state @ G_9 @ ( insert528405184_state @ ( hoare_858012674_state @ Q_6 @ D_3 @ R_1 ) @ bot_bo19817387tate_o ) )
       => ( hoare_90032982_state @ G_9 @ ( insert528405184_state @ ( hoare_858012674_state @ P_11 @ ( semi @ C_36 @ D_3 ) @ R_1 ) @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_693_WTs__elim__cases_I6_J,axiom,(
    ! [B_82: state > $o,C_34: com] :
      ( ( wt @ ( while @ B_82 @ C_34 ) )
     => ( wt @ C_34 ) ) )).

thf(fact_694_WTs__elim__cases_I4_J,axiom,(
    ! [C1: com,C2: com] :
      ( ( wt @ ( semi @ C1 @ C2 ) )
     => ~ ( ( wt @ C1 )
         => ~ ( wt @ C2 ) ) ) )).

thf(fact_695_folding__one__idem_Oidem,axiom,(
    ! [X_53: hoare_1708887482_state,F_51: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_50: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1347568576_state @ F_51 @ F_50 )
     => ( ( F_51 @ X_53 @ X_53 )
        = X_53 ) ) )).

thf(fact_696_folding__one__idem_Oidem,axiom,(
    ! [X_53: pname,F_51: pname > pname > pname,F_50: ( pname > $o ) > pname] :
      ( ( finite89670078_pname @ F_51 @ F_50 )
     => ( ( F_51 @ X_53 @ X_53 )
        = X_53 ) ) )).

thf(fact_697_com_Osimps_I12_J,axiom,(
    ! [Com1_1: com,Com2_1: com] :
      ( skip
     != ( semi @ Com1_1 @ Com2_1 ) ) )).

thf(fact_698_com_Osimps_I16_J,axiom,(
    ! [Fun_1: state > $o,Com_2: com] :
      ( skip
     != ( while @ Fun_1 @ Com_2 ) ) )).

thf(fact_699_com_Osimps_I13_J,axiom,(
    ! [Com1_1: com,Com2_1: com] :
      ( ( semi @ Com1_1 @ Com2_1 )
     != skip ) )).

thf(fact_700_com_Osimps_I17_J,axiom,(
    ! [Fun_1: state > $o,Com_2: com] :
      ( ( while @ Fun_1 @ Com_2 )
     != skip ) )).

thf(fact_701_com_Osimps_I46_J,axiom,(
    ! [Com1: com,Com2: com,Fun_1: state > $o,Com_2: com] :
      ( ( semi @ Com1 @ Com2 )
     != ( while @ Fun_1 @ Com_2 ) ) )).

thf(fact_702_com_Osimps_I47_J,axiom,(
    ! [Fun_1: state > $o,Com_2: com,Com1: com,Com2: com] :
      ( ( while @ Fun_1 @ Com_2 )
     != ( semi @ Com1 @ Com2 ) ) )).

thf(fact_703_com_Osimps_I3_J,axiom,(
    ! [Com1: com,Com2: com,Com1_1: com,Com2_1: com] :
      ( ( ( semi @ Com1 @ Com2 )
        = ( semi @ Com1_1 @ Com2_1 ) )
    <=> ( ( Com1 = Com1_1 )
        & ( Com2 = Com2_1 ) ) ) )).

thf(fact_704_com_Osimps_I5_J,axiom,(
    ! [Fun: state > $o,Com_1: com,Fun_1: state > $o,Com_2: com] :
      ( ( ( while @ Fun @ Com_1 )
        = ( while @ Fun_1 @ Com_2 ) )
    <=> ( ( Fun = Fun_1 )
        & ( Com_1 = Com_2 ) ) ) )).

thf(fact_705_com_Osimps_I59_J,axiom,(
    ! [Pname: pname,Fun: state > $o,Com_1: com] :
      ( ( body_1 @ Pname )
     != ( while @ Fun @ Com_1 ) ) )).

thf(fact_706_com_Osimps_I58_J,axiom,(
    ! [Fun: state > $o,Com_1: com,Pname: pname] :
      ( ( while @ Fun @ Com_1 )
     != ( body_1 @ Pname ) ) )).

thf(fact_707_While,axiom,(
    ! [B_82: state > $o,C_34: com] :
      ( ( wt @ C_34 )
     => ( wt @ ( while @ B_82 @ C_34 ) ) ) )).

thf(fact_708_com_Osimps_I49_J,axiom,(
    ! [Pname: pname,Com1: com,Com2: com] :
      ( ( body_1 @ Pname )
     != ( semi @ Com1 @ Com2 ) ) )).

thf(fact_709_com_Osimps_I48_J,axiom,(
    ! [Com1: com,Com2: com,Pname: pname] :
      ( ( semi @ Com1 @ Com2 )
     != ( body_1 @ Pname ) ) )).

thf(fact_710_WT_OSemi,axiom,(
    ! [C1: com,C0: com] :
      ( ( wt @ C0 )
     => ( ( wt @ C1 )
       => ( wt @ ( semi @ C0 @ C1 ) ) ) ) )).

thf(fact_711_com_Osimps_I18_J,axiom,(
    ! [Pname: pname] :
      ( skip
     != ( body_1 @ Pname ) ) )).

thf(fact_712_com_Osimps_I19_J,axiom,(
    ! [Pname: pname] :
      ( ( body_1 @ Pname )
     != skip ) )).

thf(fact_713_WT_OSkip,axiom,
    ( wt @ skip )).

thf(fact_714_folding__one__idem_Oin__idem,axiom,(
    ! [X_52: com,A_136: com > $o,F_49: com > com > com,F_48: ( com > $o ) > com] :
      ( ( finite666746948em_com @ F_49 @ F_48 )
     => ( ( finite_finite_com @ A_136 )
       => ( ( member_com @ X_52 @ A_136 )
         => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
            = ( F_48 @ A_136 ) ) ) ) ) )).

thf(fact_715_folding__one__idem_Oin__idem,axiom,(
    ! [X_52: pname,A_136: pname > $o,F_49: pname > pname > pname,F_48: ( pname > $o ) > pname] :
      ( ( finite89670078_pname @ F_49 @ F_48 )
     => ( ( finite_finite_pname @ A_136 )
       => ( ( member_pname @ X_52 @ A_136 )
         => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
            = ( F_48 @ A_136 ) ) ) ) ) )).

thf(fact_716_folding__one__idem_Oin__idem,axiom,(
    ! [X_52: hoare_1708887482_state,A_136: hoare_1708887482_state > $o,F_49: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_48: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1347568576_state @ F_49 @ F_48 )
     => ( ( finite1625599783_state @ A_136 )
       => ( ( member451959335_state @ X_52 @ A_136 )
         => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
            = ( F_48 @ A_136 ) ) ) ) ) )).

thf(fact_717_folding__one__idem_Oin__idem,axiom,(
    ! [X_52: pname > $o,A_136: ( pname > $o ) > $o,F_49: ( pname > $o ) > ( pname > $o ) > pname > $o,F_48: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite697516351name_o @ F_49 @ F_48 )
     => ( ( finite297249702name_o @ A_136 )
       => ( ( member_pname_o @ X_52 @ A_136 )
         => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
            = ( F_48 @ A_136 ) ) ) ) ) )).

thf(fact_718_folding__one__idem_Oin__idem,axiom,(
    ! [X_52: hoare_1708887482_state > $o,A_136: ( hoare_1708887482_state > $o ) > $o,F_49: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_48: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite621643279tate_o @ F_49 @ F_48 )
     => ( ( finite1329924456tate_o @ A_136 )
       => ( ( member814030440tate_o @ X_52 @ A_136 )
         => ( ( F_49 @ X_52 @ ( F_48 @ A_136 ) )
            = ( F_48 @ A_136 ) ) ) ) ) )).

thf(fact_719_folding__one__idem_Ohom__commute,axiom,(
    ! [N_1: ( pname > $o ) > $o,H_1: ( pname > $o ) > pname > $o,F_47: ( pname > $o ) > ( pname > $o ) > pname > $o,F_46: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite697516351name_o @ F_47 @ F_46 )
     => ( ! [X_3: pname > $o,Y_4: pname > $o] :
            ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
            = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
       => ( ( finite297249702name_o @ N_1 )
         => ( ( N_1 != bot_bot_pname_o_o )
           => ( ( H_1 @ ( F_46 @ N_1 ) )
              = ( F_46 @ ( image_1085733413name_o @ H_1 @ N_1 ) ) ) ) ) ) ) )).

thf(fact_720_folding__one__idem_Ohom__commute,axiom,(
    ! [N_1: ( hoare_1708887482_state > $o ) > $o,H_1: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_47: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_46: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite621643279tate_o @ F_47 @ F_46 )
     => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] :
            ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
            = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
       => ( ( finite1329924456tate_o @ N_1 )
         => ( ( N_1 != bot_bo1678742418te_o_o )
           => ( ( H_1 @ ( F_46 @ N_1 ) )
              = ( F_46 @ ( image_909543877tate_o @ H_1 @ N_1 ) ) ) ) ) ) ) )).

thf(fact_721_folding__one__idem_Ohom__commute,axiom,(
    ! [N_1: pname > $o,H_1: pname > pname,F_47: pname > pname > pname,F_46: ( pname > $o ) > pname] :
      ( ( finite89670078_pname @ F_47 @ F_46 )
     => ( ! [X_3: pname,Y_4: pname] :
            ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
            = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
       => ( ( finite_finite_pname @ N_1 )
         => ( ( N_1 != bot_bot_pname_o )
           => ( ( H_1 @ ( F_46 @ N_1 ) )
              = ( F_46 @ ( image_pname_pname @ H_1 @ N_1 ) ) ) ) ) ) ) )).

thf(fact_722_folding__one__idem_Ohom__commute,axiom,(
    ! [N_1: hoare_1708887482_state > $o,H_1: hoare_1708887482_state > hoare_1708887482_state,F_47: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_46: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1347568576_state @ F_47 @ F_46 )
     => ( ! [X_3: hoare_1708887482_state,Y_4: hoare_1708887482_state] :
            ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
            = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
       => ( ( finite1625599783_state @ N_1 )
         => ( ( N_1 != bot_bo19817387tate_o )
           => ( ( H_1 @ ( F_46 @ N_1 ) )
              = ( F_46 @ ( image_757158439_state @ H_1 @ N_1 ) ) ) ) ) ) ) )).

thf(fact_723_folding__one__idem_Ohom__commute,axiom,(
    ! [N_1: com > $o,H_1: com > com,F_47: com > com > com,F_46: ( com > $o ) > com] :
      ( ( finite666746948em_com @ F_47 @ F_46 )
     => ( ! [X_3: com,Y_4: com] :
            ( ( H_1 @ ( F_47 @ X_3 @ Y_4 ) )
            = ( F_47 @ ( H_1 @ X_3 ) @ ( H_1 @ Y_4 ) ) )
       => ( ( finite_finite_com @ N_1 )
         => ( ( N_1 != bot_bot_com_o )
           => ( ( H_1 @ ( F_46 @ N_1 ) )
              = ( F_46 @ ( image_com_com @ H_1 @ N_1 ) ) ) ) ) ) ) )).

thf(fact_724_the__elem__def,axiom,(
    ! [X_51: com > $o] :
      ( ( the_elem_com @ X_51 )
      = ( the_com_1
        @ ^ [X_3: com] :
            ( X_51
            = ( insert_com @ X_3 @ bot_bot_com_o ) ) ) ) )).

thf(fact_725_the__elem__def,axiom,(
    ! [X_51: pname > $o] :
      ( ( the_elem_pname @ X_51 )
      = ( the_pname
        @ ^ [X_3: pname] :
            ( X_51
            = ( insert_pname @ X_3 @ bot_bot_pname_o ) ) ) ) )).

thf(fact_726_the__elem__def,axiom,(
    ! [X_51: hoare_1708887482_state > $o] :
      ( ( the_el864710747_state @ X_51 )
      = ( the_Ho851197897_state
        @ ^ [X_3: hoare_1708887482_state] :
            ( X_51
            = ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_727_folding__one_Oinsert,axiom,(
    ! [X_50: com,A_135: com > $o,F_45: com > com > com,F_44: ( com > $o ) > com] :
      ( ( finite860057415ne_com @ F_45 @ F_44 )
     => ( ( finite_finite_com @ A_135 )
       => ( ~ ( member_com @ X_50 @ A_135 )
         => ( ( A_135 != bot_bot_com_o )
           => ( ( F_44 @ ( insert_com @ X_50 @ A_135 ) )
              = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) )).

thf(fact_728_folding__one_Oinsert,axiom,(
    ! [X_50: pname,A_135: pname > $o,F_45: pname > pname > pname,F_44: ( pname > $o ) > pname] :
      ( ( finite1282449217_pname @ F_45 @ F_44 )
     => ( ( finite_finite_pname @ A_135 )
       => ( ~ ( member_pname @ X_50 @ A_135 )
         => ( ( A_135 != bot_bot_pname_o )
           => ( ( F_44 @ ( insert_pname @ X_50 @ A_135 ) )
              = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) )).

thf(fact_729_folding__one_Oinsert,axiom,(
    ! [X_50: hoare_1708887482_state,A_135: hoare_1708887482_state > $o,F_45: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_44: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1615457021_state @ F_45 @ F_44 )
     => ( ( finite1625599783_state @ A_135 )
       => ( ~ ( member451959335_state @ X_50 @ A_135 )
         => ( ( A_135 != bot_bo19817387tate_o )
           => ( ( F_44 @ ( insert528405184_state @ X_50 @ A_135 ) )
              = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) )).

thf(fact_730_folding__one_Oinsert,axiom,(
    ! [X_50: pname > $o,A_135: ( pname > $o ) > $o,F_45: ( pname > $o ) > ( pname > $o ) > pname > $o,F_44: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite349908348name_o @ F_45 @ F_44 )
     => ( ( finite297249702name_o @ A_135 )
       => ( ~ ( member_pname_o @ X_50 @ A_135 )
         => ( ( A_135 != bot_bot_pname_o_o )
           => ( ( F_44 @ ( insert_pname_o @ X_50 @ A_135 ) )
              = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) )).

thf(fact_731_folding__one_Oinsert,axiom,(
    ! [X_50: hoare_1708887482_state > $o,A_135: ( hoare_1708887482_state > $o ) > $o,F_45: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_44: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite928843026tate_o @ F_45 @ F_44 )
     => ( ( finite1329924456tate_o @ A_135 )
       => ( ~ ( member814030440tate_o @ X_50 @ A_135 )
         => ( ( A_135 != bot_bo1678742418te_o_o )
           => ( ( F_44 @ ( insert949073679tate_o @ X_50 @ A_135 ) )
              = ( F_45 @ X_50 @ ( F_44 @ A_135 ) ) ) ) ) ) ) )).

thf(fact_732_triple_Oexhaust,axiom,(
    ! [Y_25: hoare_1708887482_state] :
      ~ ! [Fun1: state > state > $o,Com: com,Fun2: state > state > $o] :
          ( Y_25
         != ( hoare_858012674_state @ Fun1 @ Com @ Fun2 ) ) )).

thf(fact_733_folding__one_Osingleton,axiom,(
    ! [X_49: com,F_43: com > com > com,F_42: ( com > $o ) > com] :
      ( ( finite860057415ne_com @ F_43 @ F_42 )
     => ( ( F_42 @ ( insert_com @ X_49 @ bot_bot_com_o ) )
        = X_49 ) ) )).

thf(fact_734_folding__one_Osingleton,axiom,(
    ! [X_49: pname,F_43: pname > pname > pname,F_42: ( pname > $o ) > pname] :
      ( ( finite1282449217_pname @ F_43 @ F_42 )
     => ( ( F_42 @ ( insert_pname @ X_49 @ bot_bot_pname_o ) )
        = X_49 ) ) )).

thf(fact_735_folding__one_Osingleton,axiom,(
    ! [X_49: hoare_1708887482_state,F_43: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_42: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1615457021_state @ F_43 @ F_42 )
     => ( ( F_42 @ ( insert528405184_state @ X_49 @ bot_bo19817387tate_o ) )
        = X_49 ) ) )).

thf(fact_736_folding__one_Oclosed,axiom,(
    ! [A_134: com > $o,F_41: com > com > com,F_40: ( com > $o ) > com] :
      ( ( finite860057415ne_com @ F_41 @ F_40 )
     => ( ( finite_finite_com @ A_134 )
       => ( ( A_134 != bot_bot_com_o )
         => ( ! [X_3: com,Y_4: com] :
                ( member_com @ ( F_41 @ X_3 @ Y_4 ) @ ( insert_com @ X_3 @ ( insert_com @ Y_4 @ bot_bot_com_o ) ) )
           => ( member_com @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) )).

thf(fact_737_folding__one_Oclosed,axiom,(
    ! [A_134: pname > $o,F_41: pname > pname > pname,F_40: ( pname > $o ) > pname] :
      ( ( finite1282449217_pname @ F_41 @ F_40 )
     => ( ( finite_finite_pname @ A_134 )
       => ( ( A_134 != bot_bot_pname_o )
         => ( ! [X_3: pname,Y_4: pname] :
                ( member_pname @ ( F_41 @ X_3 @ Y_4 ) @ ( insert_pname @ X_3 @ ( insert_pname @ Y_4 @ bot_bot_pname_o ) ) )
           => ( member_pname @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) )).

thf(fact_738_folding__one_Oclosed,axiom,(
    ! [A_134: hoare_1708887482_state > $o,F_41: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_40: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1615457021_state @ F_41 @ F_40 )
     => ( ( finite1625599783_state @ A_134 )
       => ( ( A_134 != bot_bo19817387tate_o )
         => ( ! [X_3: hoare_1708887482_state,Y_4: hoare_1708887482_state] :
                ( member451959335_state @ ( F_41 @ X_3 @ Y_4 ) @ ( insert528405184_state @ X_3 @ ( insert528405184_state @ Y_4 @ bot_bo19817387tate_o ) ) )
           => ( member451959335_state @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) )).

thf(fact_739_folding__one_Oclosed,axiom,(
    ! [A_134: ( pname > $o ) > $o,F_41: ( pname > $o ) > ( pname > $o ) > pname > $o,F_40: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite349908348name_o @ F_41 @ F_40 )
     => ( ( finite297249702name_o @ A_134 )
       => ( ( A_134 != bot_bot_pname_o_o )
         => ( ! [X_3: pname > $o,Y_4: pname > $o] :
                ( member_pname_o @ ( F_41 @ X_3 @ Y_4 ) @ ( insert_pname_o @ X_3 @ ( insert_pname_o @ Y_4 @ bot_bot_pname_o_o ) ) )
           => ( member_pname_o @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) )).

thf(fact_740_folding__one_Oclosed,axiom,(
    ! [A_134: ( hoare_1708887482_state > $o ) > $o,F_41: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_40: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite928843026tate_o @ F_41 @ F_40 )
     => ( ( finite1329924456tate_o @ A_134 )
       => ( ( A_134 != bot_bo1678742418te_o_o )
         => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] :
                ( member814030440tate_o @ ( F_41 @ X_3 @ Y_4 ) @ ( insert949073679tate_o @ X_3 @ ( insert949073679tate_o @ Y_4 @ bot_bo1678742418te_o_o ) ) )
           => ( member814030440tate_o @ ( F_40 @ A_134 ) @ A_134 ) ) ) ) ) )).

thf(fact_741_image__cong,axiom,(
    ! [F_39: pname > hoare_1708887482_state,G_8: pname > hoare_1708887482_state,M_3: pname > $o,N: pname > $o] :
      ( ( M_3 = N )
     => ( ! [X_3: pname] :
            ( ( member_pname @ X_3 @ N )
           => ( ( F_39 @ X_3 )
              = ( G_8 @ X_3 ) ) )
       => ( ( image_1116629049_state @ F_39 @ M_3 )
          = ( image_1116629049_state @ G_8 @ N ) ) ) ) )).

thf(fact_742_Collect__mono,axiom,(
    ! [Q_5: hoare_1708887482_state > $o,P_10: hoare_1708887482_state > $o] :
      ( ! [X_3: hoare_1708887482_state] :
          ( ( P_10 @ X_3 )
         => ( Q_5 @ X_3 ) )
     => ( ord_le777019615tate_o @ ( collec1568722789_state @ P_10 ) @ ( collec1568722789_state @ Q_5 ) ) ) )).

thf(fact_743_Collect__mono,axiom,(
    ! [Q_5: pname > $o,P_10: pname > $o] :
      ( ! [X_3: pname] :
          ( ( P_10 @ X_3 )
         => ( Q_5 @ X_3 ) )
     => ( ord_less_eq_pname_o @ ( collect_pname @ P_10 ) @ ( collect_pname @ Q_5 ) ) ) )).

thf(fact_744_Collect__mono,axiom,(
    ! [Q_5: ( pname > $o ) > $o,P_10: ( pname > $o ) > $o] :
      ( ! [X_3: pname > $o] :
          ( ( P_10 @ X_3 )
         => ( Q_5 @ X_3 ) )
     => ( ord_le1205211808me_o_o @ ( collect_pname_o @ P_10 ) @ ( collect_pname_o @ Q_5 ) ) ) )).

thf(fact_745_Collect__mono,axiom,(
    ! [Q_5: ( hoare_1708887482_state > $o ) > $o,P_10: ( hoare_1708887482_state > $o ) > $o] :
      ( ! [X_3: hoare_1708887482_state > $o] :
          ( ( P_10 @ X_3 )
         => ( Q_5 @ X_3 ) )
     => ( ord_le1728773982te_o_o @ ( collec219771562tate_o @ P_10 ) @ ( collec219771562tate_o @ Q_5 ) ) ) )).

thf(fact_746_predicate1I,axiom,(
    ! [Q_4: pname > $o,P_9: pname > $o] :
      ( ! [X_3: pname] :
          ( ( P_9 @ X_3 )
         => ( Q_4 @ X_3 ) )
     => ( ord_less_eq_pname_o @ P_9 @ Q_4 ) ) )).

thf(fact_747_predicate1I,axiom,(
    ! [Q_4: hoare_1708887482_state > $o,P_9: hoare_1708887482_state > $o] :
      ( ! [X_3: hoare_1708887482_state] :
          ( ( P_9 @ X_3 )
         => ( Q_4 @ X_3 ) )
     => ( ord_le777019615tate_o @ P_9 @ Q_4 ) ) )).

thf(fact_748_mk__disjoint__insert,axiom,(
    ! [A_133: com,A_132: com > $o] :
      ( ( member_com @ A_133 @ A_132 )
     => ? [B_84: com > $o] :
          ( ( A_132
            = ( insert_com @ A_133 @ B_84 ) )
          & ~ ( member_com @ A_133 @ B_84 ) ) ) )).

thf(fact_749_mk__disjoint__insert,axiom,(
    ! [A_133: pname,A_132: pname > $o] :
      ( ( member_pname @ A_133 @ A_132 )
     => ? [B_84: pname > $o] :
          ( ( A_132
            = ( insert_pname @ A_133 @ B_84 ) )
          & ~ ( member_pname @ A_133 @ B_84 ) ) ) )).

thf(fact_750_mk__disjoint__insert,axiom,(
    ! [A_133: hoare_1708887482_state,A_132: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ A_133 @ A_132 )
     => ? [B_84: hoare_1708887482_state > $o] :
          ( ( A_132
            = ( insert528405184_state @ A_133 @ B_84 ) )
          & ~ ( member451959335_state @ A_133 @ B_84 ) ) ) )).

thf(fact_751_Set_Oset__insert,axiom,(
    ! [X_48: com,A_131: com > $o] :
      ( ( member_com @ X_48 @ A_131 )
     => ~ ! [B_84: com > $o] :
            ( ( A_131
              = ( insert_com @ X_48 @ B_84 ) )
           => ( member_com @ X_48 @ B_84 ) ) ) )).

thf(fact_752_Set_Oset__insert,axiom,(
    ! [X_48: pname,A_131: pname > $o] :
      ( ( member_pname @ X_48 @ A_131 )
     => ~ ! [B_84: pname > $o] :
            ( ( A_131
              = ( insert_pname @ X_48 @ B_84 ) )
           => ( member_pname @ X_48 @ B_84 ) ) ) )).

thf(fact_753_Set_Oset__insert,axiom,(
    ! [X_48: hoare_1708887482_state,A_131: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ X_48 @ A_131 )
     => ~ ! [B_84: hoare_1708887482_state > $o] :
            ( ( A_131
              = ( insert528405184_state @ X_48 @ B_84 ) )
           => ( member451959335_state @ X_48 @ B_84 ) ) ) )).

thf(fact_754_equals0I,axiom,(
    ! [A_130: com > $o] :
      ( ! [Y_4: com] :
          ~ ( member_com @ Y_4 @ A_130 )
     => ( A_130 = bot_bot_com_o ) ) )).

thf(fact_755_equals0I,axiom,(
    ! [A_130: pname > $o] :
      ( ! [Y_4: pname] :
          ~ ( member_pname @ Y_4 @ A_130 )
     => ( A_130 = bot_bot_pname_o ) ) )).

thf(fact_756_equals0I,axiom,(
    ! [A_130: hoare_1708887482_state > $o] :
      ( ! [Y_4: hoare_1708887482_state] :
          ~ ( member451959335_state @ Y_4 @ A_130 )
     => ( A_130 = bot_bo19817387tate_o ) ) )).

thf(fact_757_MGT__alternD,axiom,(
    ! [G_7: hoare_1708887482_state > $o,C_34: com] :
      ( hoare_1160767572gleton
     => ( ( hoare_90032982_state @ G_7
          @ ( insert528405184_state
            @ ( hoare_858012674_state
              @ ^ [Z_11: state,S0_1: state] :
                ! [S1: state] :
                  ( (=>) @ ( evalc @ C_34 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
              @ C_34
              @ fequal_state )
            @ bot_bo19817387tate_o ) )
       => ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_758_xt1_I15_J,axiom,(
    ! [C_35: $o,F_38: $o > $o,B_83: $o,A_129: $o] :
      ( ( A_129
      <=> ( F_38 @ B_83 ) )
     => ( ( ord_less_eq_o @ C_35 @ B_83 )
       => ( ! [X_3: $o,Y_4: $o] :
              ( ( ord_less_eq_o @ Y_4 @ X_3 )
             => ( ord_less_eq_o @ ( F_38 @ Y_4 ) @ ( F_38 @ X_3 ) ) )
         => ( ord_less_eq_o @ ( F_38 @ C_35 ) @ A_129 ) ) ) ) )).

thf(fact_759_xt1_I15_J,axiom,(
    ! [C_35: pname > $o,A_129: pname > $o,F_38: ( pname > $o ) > pname > $o,B_83: pname > $o] :
      ( ( A_129
        = ( F_38 @ B_83 ) )
     => ( ( ord_less_eq_pname_o @ C_35 @ B_83 )
       => ( ! [X_3: pname > $o,Y_4: pname > $o] :
              ( ( ord_less_eq_pname_o @ Y_4 @ X_3 )
             => ( ord_less_eq_pname_o @ ( F_38 @ Y_4 ) @ ( F_38 @ X_3 ) ) )
         => ( ord_less_eq_pname_o @ ( F_38 @ C_35 ) @ A_129 ) ) ) ) )).

thf(fact_760_xt1_I15_J,axiom,(
    ! [C_35: hoare_1708887482_state > $o,A_129: hoare_1708887482_state > $o,F_38: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,B_83: hoare_1708887482_state > $o] :
      ( ( A_129
        = ( F_38 @ B_83 ) )
     => ( ( ord_le777019615tate_o @ C_35 @ B_83 )
       => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] :
              ( ( ord_le777019615tate_o @ Y_4 @ X_3 )
             => ( ord_le777019615tate_o @ ( F_38 @ Y_4 ) @ ( F_38 @ X_3 ) ) )
         => ( ord_le777019615tate_o @ ( F_38 @ C_35 ) @ A_129 ) ) ) ) )).

thf(fact_761_MGT__alternI,axiom,(
    ! [G_7: hoare_1708887482_state > $o,C_34: com] :
      ( ( hoare_90032982_state @ G_7 @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ C_34 ) @ bot_bo19817387tate_o ) )
     => ( hoare_90032982_state @ G_7
        @ ( insert528405184_state
          @ ( hoare_858012674_state
            @ ^ [Z_11: state,S0_1: state] :
              ! [S1: state] :
                ( (=>) @ ( evalc @ C_34 @ S0_1 @ S1 ) @ ( Z_11 = S1 ) )
            @ C_34
            @ fequal_state )
          @ bot_bo19817387tate_o ) ) ) )).

thf(fact_762_MGT__def,axiom,(
    ! [C_34: com] :
      ( ( hoare_Mirabelle_MGT @ C_34 )
      = ( hoare_858012674_state @ fequal_state @ C_34 @ ( evalc @ C_34 ) ) ) )).

thf(fact_763_evalc__elim__cases_I6_J,axiom,(
    ! [P: pname,S_4: state,S1_1: state] :
      ( ( evalc @ ( body_1 @ P ) @ S_4 @ S1_1 )
     => ( evalc @ ( the_com @ ( body @ P ) ) @ S_4 @ S1_1 ) ) )).

thf(fact_764_evalc_OBody,axiom,(
    ! [Pn_1: pname,S0: state,S1_1: state] :
      ( ( evalc @ ( the_com @ ( body @ Pn_1 ) ) @ S0 @ S1_1 )
     => ( evalc @ ( body_1 @ Pn_1 ) @ S0 @ S1_1 ) ) )).

thf(fact_765_evalc__elim__cases_I1_J,axiom,(
    ! [S_4: state,T: state] :
      ( ( evalc @ skip @ S_4 @ T )
     => ( T = S_4 ) ) )).

thf(fact_766_evalc_OSkip,axiom,(
    ! [S_4: state] :
      ( evalc @ skip @ S_4 @ S_4 ) )).

thf(fact_767_evalc_OSemi,axiom,(
    ! [C1: com,S2: state,C0: com,S0: state,S1_1: state] :
      ( ( evalc @ C0 @ S0 @ S1_1 )
     => ( ( evalc @ C1 @ S1_1 @ S2 )
       => ( evalc @ ( semi @ C0 @ C1 ) @ S0 @ S2 ) ) ) )).

thf(fact_768_evalc_OWhileTrue,axiom,(
    ! [S2: state,C_34: com,S1_1: state,B_82: state > $o,S0: state] :
      ( ( B_82 @ S0 )
     => ( ( evalc @ C_34 @ S0 @ S1_1 )
       => ( ( evalc @ ( while @ B_82 @ C_34 ) @ S1_1 @ S2 )
         => ( evalc @ ( while @ B_82 @ C_34 ) @ S0 @ S2 ) ) ) ) )).

thf(fact_769_evalc_OWhileFalse,axiom,(
    ! [C_34: com,B_82: state > $o,S_4: state] :
      ( ~ ( B_82 @ S_4 )
     => ( evalc @ ( while @ B_82 @ C_34 ) @ S_4 @ S_4 ) ) )).

thf(fact_770_com__det,axiom,(
    ! [U: state,C_34: com,S_4: state,T: state] :
      ( ( evalc @ C_34 @ S_4 @ T )
     => ( ( evalc @ C_34 @ S_4 @ U )
       => ( U = T ) ) ) )).

thf(fact_771_evalc__elim__cases_I4_J,axiom,(
    ! [C1: com,C2: com,S_4: state,T: state] :
      ( ( evalc @ ( semi @ C1 @ C2 ) @ S_4 @ T )
     => ~ ! [S1: state] :
            ( ( evalc @ C1 @ S_4 @ S1 )
           => ~ ( evalc @ C2 @ S1 @ T ) ) ) )).

thf(fact_772_evalc__WHILE__case,axiom,(
    ! [B_82: state > $o,C_34: com,S_4: state,T: state] :
      ( ( evalc @ ( while @ B_82 @ C_34 ) @ S_4 @ T )
     => ( ( ( T = S_4 )
         => ( B_82 @ S_4 ) )
       => ~ ( ( B_82 @ S_4 )
           => ! [S1: state] :
                ( ( evalc @ C_34 @ S_4 @ S1 )
               => ~ ( evalc @ ( while @ B_82 @ C_34 ) @ S1 @ T ) ) ) ) ) )).

thf(fact_773_xt1_I16_J,axiom,(
    ! [C_33: $o,F_37: $o > $o,B_81: $o,A_128: $o] :
      ( ( ord_less_eq_o @ B_81 @ A_128 )
     => ( ( ( F_37 @ B_81 )
        <=> C_33 )
       => ( ! [X_3: $o,Y_4: $o] :
              ( ( ord_less_eq_o @ Y_4 @ X_3 )
             => ( ord_less_eq_o @ ( F_37 @ Y_4 ) @ ( F_37 @ X_3 ) ) )
         => ( ord_less_eq_o @ C_33 @ ( F_37 @ A_128 ) ) ) ) ) )).

thf(fact_774_xt1_I16_J,axiom,(
    ! [F_37: ( pname > $o ) > pname > $o,C_33: pname > $o,B_81: pname > $o,A_128: pname > $o] :
      ( ( ord_less_eq_pname_o @ B_81 @ A_128 )
     => ( ( ( F_37 @ B_81 )
          = C_33 )
       => ( ! [X_3: pname > $o,Y_4: pname > $o] :
              ( ( ord_less_eq_pname_o @ Y_4 @ X_3 )
             => ( ord_less_eq_pname_o @ ( F_37 @ Y_4 ) @ ( F_37 @ X_3 ) ) )
         => ( ord_less_eq_pname_o @ C_33 @ ( F_37 @ A_128 ) ) ) ) ) )).

thf(fact_775_xt1_I16_J,axiom,(
    ! [F_37: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,C_33: hoare_1708887482_state > $o,B_81: hoare_1708887482_state > $o,A_128: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ B_81 @ A_128 )
     => ( ( ( F_37 @ B_81 )
          = C_33 )
       => ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o] :
              ( ( ord_le777019615tate_o @ Y_4 @ X_3 )
             => ( ord_le777019615tate_o @ ( F_37 @ Y_4 ) @ ( F_37 @ X_3 ) ) )
         => ( ord_le777019615tate_o @ C_33 @ ( F_37 @ A_128 ) ) ) ) ) )).

thf(fact_776_folding__one_Ounion__inter,axiom,(
    ! [B_80: ( pname > $o ) > $o,A_127: ( pname > $o ) > $o,F_36: ( pname > $o ) > ( pname > $o ) > pname > $o,F_35: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite349908348name_o @ F_36 @ F_35 )
     => ( ( finite297249702name_o @ A_127 )
       => ( ( finite297249702name_o @ B_80 )
         => ( ( ( semila2013987940me_o_o @ A_127 @ B_80 )
             != bot_bot_pname_o_o )
           => ( ( F_36 @ ( F_35 @ ( semila181081674me_o_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila2013987940me_o_o @ A_127 @ B_80 ) ) )
              = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) )).

thf(fact_777_folding__one_Ounion__inter,axiom,(
    ! [B_80: ( hoare_1708887482_state > $o ) > $o,A_127: ( hoare_1708887482_state > $o ) > $o,F_36: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_35: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite928843026tate_o @ F_36 @ F_35 )
     => ( ( finite1329924456tate_o @ A_127 )
       => ( ( finite1329924456tate_o @ B_80 )
         => ( ( ( semila598060698te_o_o @ A_127 @ B_80 )
             != bot_bo1678742418te_o_o )
           => ( ( F_36 @ ( F_35 @ ( semila1853742644te_o_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila598060698te_o_o @ A_127 @ B_80 ) ) )
              = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) )).

thf(fact_778_folding__one_Ounion__inter,axiom,(
    ! [B_80: pname > $o,A_127: pname > $o,F_36: pname > pname > pname,F_35: ( pname > $o ) > pname] :
      ( ( finite1282449217_pname @ F_36 @ F_35 )
     => ( ( finite_finite_pname @ A_127 )
       => ( ( finite_finite_pname @ B_80 )
         => ( ( ( semila1673364395name_o @ A_127 @ B_80 )
             != bot_bot_pname_o )
           => ( ( F_36 @ ( F_35 @ ( semila1780557381name_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila1673364395name_o @ A_127 @ B_80 ) ) )
              = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) )).

thf(fact_779_folding__one_Ounion__inter,axiom,(
    ! [B_80: hoare_1708887482_state > $o,A_127: hoare_1708887482_state > $o,F_36: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_35: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1615457021_state @ F_36 @ F_35 )
     => ( ( finite1625599783_state @ A_127 )
       => ( ( finite1625599783_state @ B_80 )
         => ( ( ( semila129691299tate_o @ A_127 @ B_80 )
             != bot_bo19817387tate_o )
           => ( ( F_36 @ ( F_35 @ ( semila1122118281tate_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila129691299tate_o @ A_127 @ B_80 ) ) )
              = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) )).

thf(fact_780_folding__one_Ounion__inter,axiom,(
    ! [B_80: com > $o,A_127: com > $o,F_36: com > com > com,F_35: ( com > $o ) > com] :
      ( ( finite860057415ne_com @ F_36 @ F_35 )
     => ( ( finite_finite_com @ A_127 )
       => ( ( finite_finite_com @ B_80 )
         => ( ( ( semila513601829_com_o @ A_127 @ B_80 )
             != bot_bot_com_o )
           => ( ( F_36 @ ( F_35 @ ( semila1562558655_com_o @ A_127 @ B_80 ) ) @ ( F_35 @ ( semila513601829_com_o @ A_127 @ B_80 ) ) )
              = ( F_36 @ ( F_35 @ A_127 ) @ ( F_35 @ B_80 ) ) ) ) ) ) ) )).

thf(fact_781_folding__one_Ounion__disjoint,axiom,(
    ! [B_79: ( pname > $o ) > $o,A_126: ( pname > $o ) > $o,F_34: ( pname > $o ) > ( pname > $o ) > pname > $o,F_33: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite349908348name_o @ F_34 @ F_33 )
     => ( ( finite297249702name_o @ A_126 )
       => ( ( A_126 != bot_bot_pname_o_o )
         => ( ( finite297249702name_o @ B_79 )
           => ( ( B_79 != bot_bot_pname_o_o )
             => ( ( ( semila2013987940me_o_o @ A_126 @ B_79 )
                  = bot_bot_pname_o_o )
               => ( ( F_33 @ ( semila181081674me_o_o @ A_126 @ B_79 ) )
                  = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) )).

thf(fact_782_folding__one_Ounion__disjoint,axiom,(
    ! [B_79: ( hoare_1708887482_state > $o ) > $o,A_126: ( hoare_1708887482_state > $o ) > $o,F_34: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_33: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite928843026tate_o @ F_34 @ F_33 )
     => ( ( finite1329924456tate_o @ A_126 )
       => ( ( A_126 != bot_bo1678742418te_o_o )
         => ( ( finite1329924456tate_o @ B_79 )
           => ( ( B_79 != bot_bo1678742418te_o_o )
             => ( ( ( semila598060698te_o_o @ A_126 @ B_79 )
                  = bot_bo1678742418te_o_o )
               => ( ( F_33 @ ( semila1853742644te_o_o @ A_126 @ B_79 ) )
                  = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) )).

thf(fact_783_folding__one_Ounion__disjoint,axiom,(
    ! [B_79: pname > $o,A_126: pname > $o,F_34: pname > pname > pname,F_33: ( pname > $o ) > pname] :
      ( ( finite1282449217_pname @ F_34 @ F_33 )
     => ( ( finite_finite_pname @ A_126 )
       => ( ( A_126 != bot_bot_pname_o )
         => ( ( finite_finite_pname @ B_79 )
           => ( ( B_79 != bot_bot_pname_o )
             => ( ( ( semila1673364395name_o @ A_126 @ B_79 )
                  = bot_bot_pname_o )
               => ( ( F_33 @ ( semila1780557381name_o @ A_126 @ B_79 ) )
                  = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) )).

thf(fact_784_folding__one_Ounion__disjoint,axiom,(
    ! [B_79: hoare_1708887482_state > $o,A_126: hoare_1708887482_state > $o,F_34: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_33: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1615457021_state @ F_34 @ F_33 )
     => ( ( finite1625599783_state @ A_126 )
       => ( ( A_126 != bot_bo19817387tate_o )
         => ( ( finite1625599783_state @ B_79 )
           => ( ( B_79 != bot_bo19817387tate_o )
             => ( ( ( semila129691299tate_o @ A_126 @ B_79 )
                  = bot_bo19817387tate_o )
               => ( ( F_33 @ ( semila1122118281tate_o @ A_126 @ B_79 ) )
                  = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) )).

thf(fact_785_folding__one_Ounion__disjoint,axiom,(
    ! [B_79: com > $o,A_126: com > $o,F_34: com > com > com,F_33: ( com > $o ) > com] :
      ( ( finite860057415ne_com @ F_34 @ F_33 )
     => ( ( finite_finite_com @ A_126 )
       => ( ( A_126 != bot_bot_com_o )
         => ( ( finite_finite_com @ B_79 )
           => ( ( B_79 != bot_bot_com_o )
             => ( ( ( semila513601829_com_o @ A_126 @ B_79 )
                  = bot_bot_com_o )
               => ( ( F_33 @ ( semila1562558655_com_o @ A_126 @ B_79 ) )
                  = ( F_34 @ ( F_33 @ A_126 ) @ ( F_33 @ B_79 ) ) ) ) ) ) ) ) ) )).

thf(fact_786_folding__one_Oinsert__remove,axiom,(
    ! [X_47: com,A_125: com > $o,F_32: com > com > com,F_31: ( com > $o ) > com] :
      ( ( finite860057415ne_com @ F_32 @ F_31 )
     => ( ( finite_finite_com @ A_125 )
       => ( ( ( ( minus_minus_com_o @ A_125 @ ( insert_com @ X_47 @ bot_bot_com_o ) )
              = bot_bot_com_o )
           => ( ( F_31 @ ( insert_com @ X_47 @ A_125 ) )
              = X_47 ) )
          & ( ( ( minus_minus_com_o @ A_125 @ ( insert_com @ X_47 @ bot_bot_com_o ) )
             != bot_bot_com_o )
           => ( ( F_31 @ ( insert_com @ X_47 @ A_125 ) )
              = ( F_32 @ X_47 @ ( F_31 @ ( minus_minus_com_o @ A_125 @ ( insert_com @ X_47 @ bot_bot_com_o ) ) ) ) ) ) ) ) ) )).

thf(fact_787_folding__one_Oinsert__remove,axiom,(
    ! [X_47: pname,A_125: pname > $o,F_32: pname > pname > pname,F_31: ( pname > $o ) > pname] :
      ( ( finite1282449217_pname @ F_32 @ F_31 )
     => ( ( finite_finite_pname @ A_125 )
       => ( ( ( ( minus_minus_pname_o @ A_125 @ ( insert_pname @ X_47 @ bot_bot_pname_o ) )
              = bot_bot_pname_o )
           => ( ( F_31 @ ( insert_pname @ X_47 @ A_125 ) )
              = X_47 ) )
          & ( ( ( minus_minus_pname_o @ A_125 @ ( insert_pname @ X_47 @ bot_bot_pname_o ) )
             != bot_bot_pname_o )
           => ( ( F_31 @ ( insert_pname @ X_47 @ A_125 ) )
              = ( F_32 @ X_47 @ ( F_31 @ ( minus_minus_pname_o @ A_125 @ ( insert_pname @ X_47 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) )).

thf(fact_788_folding__one_Oinsert__remove,axiom,(
    ! [X_47: hoare_1708887482_state,A_125: hoare_1708887482_state > $o,F_32: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_31: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1615457021_state @ F_32 @ F_31 )
     => ( ( finite1625599783_state @ A_125 )
       => ( ( ( ( minus_2056855718tate_o @ A_125 @ ( insert528405184_state @ X_47 @ bot_bo19817387tate_o ) )
              = bot_bo19817387tate_o )
           => ( ( F_31 @ ( insert528405184_state @ X_47 @ A_125 ) )
              = X_47 ) )
          & ( ( ( minus_2056855718tate_o @ A_125 @ ( insert528405184_state @ X_47 @ bot_bo19817387tate_o ) )
             != bot_bo19817387tate_o )
           => ( ( F_31 @ ( insert528405184_state @ X_47 @ A_125 ) )
              = ( F_32 @ X_47 @ ( F_31 @ ( minus_2056855718tate_o @ A_125 @ ( insert528405184_state @ X_47 @ bot_bo19817387tate_o ) ) ) ) ) ) ) ) ) )).

thf(fact_789_folding__one_Oinsert__remove,axiom,(
    ! [X_47: pname > $o,A_125: ( pname > $o ) > $o,F_32: ( pname > $o ) > ( pname > $o ) > pname > $o,F_31: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite349908348name_o @ F_32 @ F_31 )
     => ( ( finite297249702name_o @ A_125 )
       => ( ( ( ( minus_1480864103me_o_o @ A_125 @ ( insert_pname_o @ X_47 @ bot_bot_pname_o_o ) )
              = bot_bot_pname_o_o )
           => ( ( F_31 @ ( insert_pname_o @ X_47 @ A_125 ) )
              = X_47 ) )
          & ( ( ( minus_1480864103me_o_o @ A_125 @ ( insert_pname_o @ X_47 @ bot_bot_pname_o_o ) )
             != bot_bot_pname_o_o )
           => ( ( F_31 @ ( insert_pname_o @ X_47 @ A_125 ) )
              = ( F_32 @ X_47 @ ( F_31 @ ( minus_1480864103me_o_o @ A_125 @ ( insert_pname_o @ X_47 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) )).

thf(fact_790_folding__one_Oinsert__remove,axiom,(
    ! [X_47: hoare_1708887482_state > $o,A_125: ( hoare_1708887482_state > $o ) > $o,F_32: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_31: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite928843026tate_o @ F_32 @ F_31 )
     => ( ( finite1329924456tate_o @ A_125 )
       => ( ( ( ( minus_548038231te_o_o @ A_125 @ ( insert949073679tate_o @ X_47 @ bot_bo1678742418te_o_o ) )
              = bot_bo1678742418te_o_o )
           => ( ( F_31 @ ( insert949073679tate_o @ X_47 @ A_125 ) )
              = X_47 ) )
          & ( ( ( minus_548038231te_o_o @ A_125 @ ( insert949073679tate_o @ X_47 @ bot_bo1678742418te_o_o ) )
             != bot_bo1678742418te_o_o )
           => ( ( F_31 @ ( insert949073679tate_o @ X_47 @ A_125 ) )
              = ( F_32 @ X_47 @ ( F_31 @ ( minus_548038231te_o_o @ A_125 @ ( insert949073679tate_o @ X_47 @ bot_bo1678742418te_o_o ) ) ) ) ) ) ) ) ) )).

thf(fact_791_folding__one_Oremove,axiom,(
    ! [X_46: com,A_124: com > $o,F_30: com > com > com,F_29: ( com > $o ) > com] :
      ( ( finite860057415ne_com @ F_30 @ F_29 )
     => ( ( finite_finite_com @ A_124 )
       => ( ( member_com @ X_46 @ A_124 )
         => ( ( ( ( minus_minus_com_o @ A_124 @ ( insert_com @ X_46 @ bot_bot_com_o ) )
                = bot_bot_com_o )
             => ( ( F_29 @ A_124 )
                = X_46 ) )
            & ( ( ( minus_minus_com_o @ A_124 @ ( insert_com @ X_46 @ bot_bot_com_o ) )
               != bot_bot_com_o )
             => ( ( F_29 @ A_124 )
                = ( F_30 @ X_46 @ ( F_29 @ ( minus_minus_com_o @ A_124 @ ( insert_com @ X_46 @ bot_bot_com_o ) ) ) ) ) ) ) ) ) ) )).

thf(fact_792_folding__one_Oremove,axiom,(
    ! [X_46: pname,A_124: pname > $o,F_30: pname > pname > pname,F_29: ( pname > $o ) > pname] :
      ( ( finite1282449217_pname @ F_30 @ F_29 )
     => ( ( finite_finite_pname @ A_124 )
       => ( ( member_pname @ X_46 @ A_124 )
         => ( ( ( ( minus_minus_pname_o @ A_124 @ ( insert_pname @ X_46 @ bot_bot_pname_o ) )
                = bot_bot_pname_o )
             => ( ( F_29 @ A_124 )
                = X_46 ) )
            & ( ( ( minus_minus_pname_o @ A_124 @ ( insert_pname @ X_46 @ bot_bot_pname_o ) )
               != bot_bot_pname_o )
             => ( ( F_29 @ A_124 )
                = ( F_30 @ X_46 @ ( F_29 @ ( minus_minus_pname_o @ A_124 @ ( insert_pname @ X_46 @ bot_bot_pname_o ) ) ) ) ) ) ) ) ) ) )).

thf(fact_793_folding__one_Oremove,axiom,(
    ! [X_46: hoare_1708887482_state,A_124: hoare_1708887482_state > $o,F_30: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_29: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1615457021_state @ F_30 @ F_29 )
     => ( ( finite1625599783_state @ A_124 )
       => ( ( member451959335_state @ X_46 @ A_124 )
         => ( ( ( ( minus_2056855718tate_o @ A_124 @ ( insert528405184_state @ X_46 @ bot_bo19817387tate_o ) )
                = bot_bo19817387tate_o )
             => ( ( F_29 @ A_124 )
                = X_46 ) )
            & ( ( ( minus_2056855718tate_o @ A_124 @ ( insert528405184_state @ X_46 @ bot_bo19817387tate_o ) )
               != bot_bo19817387tate_o )
             => ( ( F_29 @ A_124 )
                = ( F_30 @ X_46 @ ( F_29 @ ( minus_2056855718tate_o @ A_124 @ ( insert528405184_state @ X_46 @ bot_bo19817387tate_o ) ) ) ) ) ) ) ) ) ) )).

thf(fact_794_folding__one_Oremove,axiom,(
    ! [X_46: pname > $o,A_124: ( pname > $o ) > $o,F_30: ( pname > $o ) > ( pname > $o ) > pname > $o,F_29: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite349908348name_o @ F_30 @ F_29 )
     => ( ( finite297249702name_o @ A_124 )
       => ( ( member_pname_o @ X_46 @ A_124 )
         => ( ( ( ( minus_1480864103me_o_o @ A_124 @ ( insert_pname_o @ X_46 @ bot_bot_pname_o_o ) )
                = bot_bot_pname_o_o )
             => ( ( F_29 @ A_124 )
                = X_46 ) )
            & ( ( ( minus_1480864103me_o_o @ A_124 @ ( insert_pname_o @ X_46 @ bot_bot_pname_o_o ) )
               != bot_bot_pname_o_o )
             => ( ( F_29 @ A_124 )
                = ( F_30 @ X_46 @ ( F_29 @ ( minus_1480864103me_o_o @ A_124 @ ( insert_pname_o @ X_46 @ bot_bot_pname_o_o ) ) ) ) ) ) ) ) ) ) )).

thf(fact_795_folding__one_Oremove,axiom,(
    ! [X_46: hoare_1708887482_state > $o,A_124: ( hoare_1708887482_state > $o ) > $o,F_30: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_29: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite928843026tate_o @ F_30 @ F_29 )
     => ( ( finite1329924456tate_o @ A_124 )
       => ( ( member814030440tate_o @ X_46 @ A_124 )
         => ( ( ( ( minus_548038231te_o_o @ A_124 @ ( insert949073679tate_o @ X_46 @ bot_bo1678742418te_o_o ) )
                = bot_bo1678742418te_o_o )
             => ( ( F_29 @ A_124 )
                = X_46 ) )
            & ( ( ( minus_548038231te_o_o @ A_124 @ ( insert949073679tate_o @ X_46 @ bot_bo1678742418te_o_o ) )
               != bot_bo1678742418te_o_o )
             => ( ( F_29 @ A_124 )
                = ( F_30 @ X_46 @ ( F_29 @ ( minus_548038231te_o_o @ A_124 @ ( insert949073679tate_o @ X_46 @ bot_bo1678742418te_o_o ) ) ) ) ) ) ) ) ) ) )).

thf(fact_796_is__none__code_I2_J,axiom,(
    ! [X_45: pname] :
      ~ ( is_none_pname @ ( some_pname @ X_45 ) ) )).

thf(fact_797_is__none__code_I2_J,axiom,(
    ! [X_45: hoare_1708887482_state] :
      ~ ( is_non163157940_state @ ( some_H1974565227_state @ X_45 ) ) )).

thf(fact_798_is__none__code_I2_J,axiom,(
    ! [X_45: com] :
      ~ ( is_none_com @ ( some_com @ X_45 ) ) )).

thf(fact_799_conseq,axiom,(
    ! [Q_2: state > state > $o,G_6: hoare_1708887482_state > $o,C_32: com,P_7: state > state > $o] :
      ( ! [Z_11: state,S_2: state] :
          ( ( P_7 @ Z_11 @ S_2 )
         => ? [P_8: state > state > $o,Q_3: state > state > $o] :
              ( ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ P_8 @ C_32 @ Q_3 ) @ bot_bo19817387tate_o ) )
              & ! [S_3: state] :
                  ( ! [Z_12: state] :
                      ( ( P_8 @ Z_12 @ S_2 )
                     => ( Q_3 @ Z_12 @ S_3 ) )
                 => ( Q_2 @ Z_11 @ S_3 ) ) ) )
     => ( hoare_90032982_state @ G_6 @ ( insert528405184_state @ ( hoare_858012674_state @ P_7 @ C_32 @ Q_2 ) @ bot_bo19817387tate_o ) ) ) )).

thf(fact_800_IntE,axiom,(
    ! [C_31: com,A_123: com > $o,B_78: com > $o] :
      ( ( member_com @ C_31 @ ( semila513601829_com_o @ A_123 @ B_78 ) )
     => ~ ( ( member_com @ C_31 @ A_123 )
         => ~ ( member_com @ C_31 @ B_78 ) ) ) )).

thf(fact_801_IntE,axiom,(
    ! [C_31: pname,A_123: pname > $o,B_78: pname > $o] :
      ( ( member_pname @ C_31 @ ( semila1673364395name_o @ A_123 @ B_78 ) )
     => ~ ( ( member_pname @ C_31 @ A_123 )
         => ~ ( member_pname @ C_31 @ B_78 ) ) ) )).

thf(fact_802_IntE,axiom,(
    ! [C_31: hoare_1708887482_state,A_123: hoare_1708887482_state > $o,B_78: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_31 @ ( semila129691299tate_o @ A_123 @ B_78 ) )
     => ~ ( ( member451959335_state @ C_31 @ A_123 )
         => ~ ( member451959335_state @ C_31 @ B_78 ) ) ) )).

thf(fact_803_IntI,axiom,(
    ! [B_77: com > $o,C_30: com,A_122: com > $o] :
      ( ( member_com @ C_30 @ A_122 )
     => ( ( member_com @ C_30 @ B_77 )
       => ( member_com @ C_30 @ ( semila513601829_com_o @ A_122 @ B_77 ) ) ) ) )).

thf(fact_804_IntI,axiom,(
    ! [B_77: pname > $o,C_30: pname,A_122: pname > $o] :
      ( ( member_pname @ C_30 @ A_122 )
     => ( ( member_pname @ C_30 @ B_77 )
       => ( member_pname @ C_30 @ ( semila1673364395name_o @ A_122 @ B_77 ) ) ) ) )).

thf(fact_805_IntI,axiom,(
    ! [B_77: hoare_1708887482_state > $o,C_30: hoare_1708887482_state,A_122: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_30 @ A_122 )
     => ( ( member451959335_state @ C_30 @ B_77 )
       => ( member451959335_state @ C_30 @ ( semila129691299tate_o @ A_122 @ B_77 ) ) ) ) )).

thf(fact_806_DiffE,axiom,(
    ! [C_29: com,A_121: com > $o,B_76: com > $o] :
      ( ( member_com @ C_29 @ ( minus_minus_com_o @ A_121 @ B_76 ) )
     => ~ ( ( member_com @ C_29 @ A_121 )
         => ( member_com @ C_29 @ B_76 ) ) ) )).

thf(fact_807_DiffE,axiom,(
    ! [C_29: pname,A_121: pname > $o,B_76: pname > $o] :
      ( ( member_pname @ C_29 @ ( minus_minus_pname_o @ A_121 @ B_76 ) )
     => ~ ( ( member_pname @ C_29 @ A_121 )
         => ( member_pname @ C_29 @ B_76 ) ) ) )).

thf(fact_808_DiffE,axiom,(
    ! [C_29: hoare_1708887482_state,A_121: hoare_1708887482_state > $o,B_76: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_29 @ ( minus_2056855718tate_o @ A_121 @ B_76 ) )
     => ~ ( ( member451959335_state @ C_29 @ A_121 )
         => ( member451959335_state @ C_29 @ B_76 ) ) ) )).

thf(fact_809_DiffI,axiom,(
    ! [B_75: com > $o,C_28: com,A_120: com > $o] :
      ( ( member_com @ C_28 @ A_120 )
     => ( ~ ( member_com @ C_28 @ B_75 )
       => ( member_com @ C_28 @ ( minus_minus_com_o @ A_120 @ B_75 ) ) ) ) )).

thf(fact_810_DiffI,axiom,(
    ! [B_75: pname > $o,C_28: pname,A_120: pname > $o] :
      ( ( member_pname @ C_28 @ A_120 )
     => ( ~ ( member_pname @ C_28 @ B_75 )
       => ( member_pname @ C_28 @ ( minus_minus_pname_o @ A_120 @ B_75 ) ) ) ) )).

thf(fact_811_DiffI,axiom,(
    ! [B_75: hoare_1708887482_state > $o,C_28: hoare_1708887482_state,A_120: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_28 @ A_120 )
     => ( ~ ( member451959335_state @ C_28 @ B_75 )
       => ( member451959335_state @ C_28 @ ( minus_2056855718tate_o @ A_120 @ B_75 ) ) ) ) )).

thf(fact_812_finite__Int,axiom,(
    ! [G_5: ( pname > $o ) > $o,F_28: ( pname > $o ) > $o] :
      ( ( ( finite297249702name_o @ F_28 )
        | ( finite297249702name_o @ G_5 ) )
     => ( finite297249702name_o @ ( semila2013987940me_o_o @ F_28 @ G_5 ) ) ) )).

thf(fact_813_finite__Int,axiom,(
    ! [G_5: ( hoare_1708887482_state > $o ) > $o,F_28: ( hoare_1708887482_state > $o ) > $o] :
      ( ( ( finite1329924456tate_o @ F_28 )
        | ( finite1329924456tate_o @ G_5 ) )
     => ( finite1329924456tate_o @ ( semila598060698te_o_o @ F_28 @ G_5 ) ) ) )).

thf(fact_814_finite__Int,axiom,(
    ! [G_5: pname > $o,F_28: pname > $o] :
      ( ( ( finite_finite_pname @ F_28 )
        | ( finite_finite_pname @ G_5 ) )
     => ( finite_finite_pname @ ( semila1673364395name_o @ F_28 @ G_5 ) ) ) )).

thf(fact_815_finite__Int,axiom,(
    ! [G_5: hoare_1708887482_state > $o,F_28: hoare_1708887482_state > $o] :
      ( ( ( finite1625599783_state @ F_28 )
        | ( finite1625599783_state @ G_5 ) )
     => ( finite1625599783_state @ ( semila129691299tate_o @ F_28 @ G_5 ) ) ) )).

thf(fact_816_finite__Diff,axiom,(
    ! [B_74: ( pname > $o ) > $o,A_119: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_119 )
     => ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_119 @ B_74 ) ) ) )).

thf(fact_817_finite__Diff,axiom,(
    ! [B_74: ( hoare_1708887482_state > $o ) > $o,A_119: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_119 )
     => ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_119 @ B_74 ) ) ) )).

thf(fact_818_finite__Diff,axiom,(
    ! [B_74: pname > $o,A_119: pname > $o] :
      ( ( finite_finite_pname @ A_119 )
     => ( finite_finite_pname @ ( minus_minus_pname_o @ A_119 @ B_74 ) ) ) )).

thf(fact_819_finite__Diff,axiom,(
    ! [B_74: hoare_1708887482_state > $o,A_119: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_119 )
     => ( finite1625599783_state @ ( minus_2056855718tate_o @ A_119 @ B_74 ) ) ) )).

thf(fact_820_inf__Int__eq,axiom,(
    ! [R: com > $o,S_1: com > $o,X_3: com] :
      ( ( semila513601829_com_o
        @ ^ [Y_4: com] :
            ( member_com @ Y_4 @ R )
        @ ^ [Y_4: com] :
            ( member_com @ Y_4 @ S_1 )
        @ X_3 )
    <=> ( member_com @ X_3 @ ( semila513601829_com_o @ R @ S_1 ) ) ) )).

thf(fact_821_inf__Int__eq,axiom,(
    ! [R: pname > $o,S_1: pname > $o,X_3: pname] :
      ( ( semila1673364395name_o
        @ ^ [Y_4: pname] :
            ( member_pname @ Y_4 @ R )
        @ ^ [Y_4: pname] :
            ( member_pname @ Y_4 @ S_1 )
        @ X_3 )
    <=> ( member_pname @ X_3 @ ( semila1673364395name_o @ R @ S_1 ) ) ) )).

thf(fact_822_inf__Int__eq,axiom,(
    ! [R: hoare_1708887482_state > $o,S_1: hoare_1708887482_state > $o,X_3: hoare_1708887482_state] :
      ( ( semila129691299tate_o
        @ ^ [Y_4: hoare_1708887482_state] :
            ( member451959335_state @ Y_4 @ R )
        @ ^ [Y_4: hoare_1708887482_state] :
            ( member451959335_state @ Y_4 @ S_1 )
        @ X_3 )
    <=> ( member451959335_state @ X_3 @ ( semila129691299tate_o @ R @ S_1 ) ) ) )).

thf(fact_823_Diff__disjoint,axiom,(
    ! [A_118: com > $o,B_73: com > $o] :
      ( ( semila513601829_com_o @ A_118 @ ( minus_minus_com_o @ B_73 @ A_118 ) )
      = bot_bot_com_o ) )).

thf(fact_824_Diff__disjoint,axiom,(
    ! [A_118: pname > $o,B_73: pname > $o] :
      ( ( semila1673364395name_o @ A_118 @ ( minus_minus_pname_o @ B_73 @ A_118 ) )
      = bot_bot_pname_o ) )).

thf(fact_825_Diff__disjoint,axiom,(
    ! [A_118: hoare_1708887482_state > $o,B_73: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ A_118 @ ( minus_2056855718tate_o @ B_73 @ A_118 ) )
      = bot_bo19817387tate_o ) )).

thf(fact_826_Diff__triv,axiom,(
    ! [A_117: com > $o,B_72: com > $o] :
      ( ( ( semila513601829_com_o @ A_117 @ B_72 )
        = bot_bot_com_o )
     => ( ( minus_minus_com_o @ A_117 @ B_72 )
        = A_117 ) ) )).

thf(fact_827_Diff__triv,axiom,(
    ! [A_117: pname > $o,B_72: pname > $o] :
      ( ( ( semila1673364395name_o @ A_117 @ B_72 )
        = bot_bot_pname_o )
     => ( ( minus_minus_pname_o @ A_117 @ B_72 )
        = A_117 ) ) )).

thf(fact_828_Diff__triv,axiom,(
    ! [A_117: hoare_1708887482_state > $o,B_72: hoare_1708887482_state > $o] :
      ( ( ( semila129691299tate_o @ A_117 @ B_72 )
        = bot_bo19817387tate_o )
     => ( ( minus_2056855718tate_o @ A_117 @ B_72 )
        = A_117 ) ) )).

thf(fact_829_DiffD2,axiom,(
    ! [C_27: com,A_116: com > $o,B_71: com > $o] :
      ( ( member_com @ C_27 @ ( minus_minus_com_o @ A_116 @ B_71 ) )
     => ~ ( member_com @ C_27 @ B_71 ) ) )).

thf(fact_830_DiffD2,axiom,(
    ! [C_27: pname,A_116: pname > $o,B_71: pname > $o] :
      ( ( member_pname @ C_27 @ ( minus_minus_pname_o @ A_116 @ B_71 ) )
     => ~ ( member_pname @ C_27 @ B_71 ) ) )).

thf(fact_831_DiffD2,axiom,(
    ! [C_27: hoare_1708887482_state,A_116: hoare_1708887482_state > $o,B_71: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_27 @ ( minus_2056855718tate_o @ A_116 @ B_71 ) )
     => ~ ( member451959335_state @ C_27 @ B_71 ) ) )).

thf(fact_832_IntD2,axiom,(
    ! [C_26: com,A_115: com > $o,B_70: com > $o] :
      ( ( member_com @ C_26 @ ( semila513601829_com_o @ A_115 @ B_70 ) )
     => ( member_com @ C_26 @ B_70 ) ) )).

thf(fact_833_IntD2,axiom,(
    ! [C_26: pname,A_115: pname > $o,B_70: pname > $o] :
      ( ( member_pname @ C_26 @ ( semila1673364395name_o @ A_115 @ B_70 ) )
     => ( member_pname @ C_26 @ B_70 ) ) )).

thf(fact_834_IntD2,axiom,(
    ! [C_26: hoare_1708887482_state,A_115: hoare_1708887482_state > $o,B_70: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_26 @ ( semila129691299tate_o @ A_115 @ B_70 ) )
     => ( member451959335_state @ C_26 @ B_70 ) ) )).

thf(fact_835_IntD1,axiom,(
    ! [C_25: com,A_114: com > $o,B_69: com > $o] :
      ( ( member_com @ C_25 @ ( semila513601829_com_o @ A_114 @ B_69 ) )
     => ( member_com @ C_25 @ A_114 ) ) )).

thf(fact_836_IntD1,axiom,(
    ! [C_25: pname,A_114: pname > $o,B_69: pname > $o] :
      ( ( member_pname @ C_25 @ ( semila1673364395name_o @ A_114 @ B_69 ) )
     => ( member_pname @ C_25 @ A_114 ) ) )).

thf(fact_837_IntD1,axiom,(
    ! [C_25: hoare_1708887482_state,A_114: hoare_1708887482_state > $o,B_69: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_25 @ ( semila129691299tate_o @ A_114 @ B_69 ) )
     => ( member451959335_state @ C_25 @ A_114 ) ) )).

thf(fact_838_DiffD1,axiom,(
    ! [C_24: com,A_113: com > $o,B_68: com > $o] :
      ( ( member_com @ C_24 @ ( minus_minus_com_o @ A_113 @ B_68 ) )
     => ( member_com @ C_24 @ A_113 ) ) )).

thf(fact_839_DiffD1,axiom,(
    ! [C_24: pname,A_113: pname > $o,B_68: pname > $o] :
      ( ( member_pname @ C_24 @ ( minus_minus_pname_o @ A_113 @ B_68 ) )
     => ( member_pname @ C_24 @ A_113 ) ) )).

thf(fact_840_DiffD1,axiom,(
    ! [C_24: hoare_1708887482_state,A_113: hoare_1708887482_state > $o,B_68: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_24 @ ( minus_2056855718tate_o @ A_113 @ B_68 ) )
     => ( member451959335_state @ C_24 @ A_113 ) ) )).

thf(fact_841_Int__iff,axiom,(
    ! [C_23: com,A_112: com > $o,B_67: com > $o] :
      ( ( member_com @ C_23 @ ( semila513601829_com_o @ A_112 @ B_67 ) )
    <=> ( ( member_com @ C_23 @ A_112 )
        & ( member_com @ C_23 @ B_67 ) ) ) )).

thf(fact_842_Int__iff,axiom,(
    ! [C_23: pname,A_112: pname > $o,B_67: pname > $o] :
      ( ( member_pname @ C_23 @ ( semila1673364395name_o @ A_112 @ B_67 ) )
    <=> ( ( member_pname @ C_23 @ A_112 )
        & ( member_pname @ C_23 @ B_67 ) ) ) )).

thf(fact_843_Int__iff,axiom,(
    ! [C_23: hoare_1708887482_state,A_112: hoare_1708887482_state > $o,B_67: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_23 @ ( semila129691299tate_o @ A_112 @ B_67 ) )
    <=> ( ( member451959335_state @ C_23 @ A_112 )
        & ( member451959335_state @ C_23 @ B_67 ) ) ) )).

thf(fact_844_Diff__iff,axiom,(
    ! [C_22: com,A_111: com > $o,B_66: com > $o] :
      ( ( member_com @ C_22 @ ( minus_minus_com_o @ A_111 @ B_66 ) )
    <=> ( ( member_com @ C_22 @ A_111 )
        & ~ ( member_com @ C_22 @ B_66 ) ) ) )).

thf(fact_845_Diff__iff,axiom,(
    ! [C_22: pname,A_111: pname > $o,B_66: pname > $o] :
      ( ( member_pname @ C_22 @ ( minus_minus_pname_o @ A_111 @ B_66 ) )
    <=> ( ( member_pname @ C_22 @ A_111 )
        & ~ ( member_pname @ C_22 @ B_66 ) ) ) )).

thf(fact_846_Diff__iff,axiom,(
    ! [C_22: hoare_1708887482_state,A_111: hoare_1708887482_state > $o,B_66: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ C_22 @ ( minus_2056855718tate_o @ A_111 @ B_66 ) )
    <=> ( ( member451959335_state @ C_22 @ A_111 )
        & ~ ( member451959335_state @ C_22 @ B_66 ) ) ) )).

thf(fact_847_Int__def,axiom,(
    ! [A_110: com > $o,B_65: com > $o] :
      ( ( semila513601829_com_o @ A_110 @ B_65 )
      = ( collect_com
        @ ^ [X_3: com] :
            ( (&) @ ( member_com @ X_3 @ A_110 ) @ ( member_com @ X_3 @ B_65 ) ) ) ) )).

thf(fact_848_Int__def,axiom,(
    ! [A_110: pname > $o,B_65: pname > $o] :
      ( ( semila1673364395name_o @ A_110 @ B_65 )
      = ( collect_pname
        @ ^ [X_3: pname] :
            ( (&) @ ( member_pname @ X_3 @ A_110 ) @ ( member_pname @ X_3 @ B_65 ) ) ) ) )).

thf(fact_849_Int__def,axiom,(
    ! [A_110: hoare_1708887482_state > $o,B_65: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ A_110 @ B_65 )
      = ( collec1568722789_state
        @ ^ [X_3: hoare_1708887482_state] :
            ( (&) @ ( member451959335_state @ X_3 @ A_110 ) @ ( member451959335_state @ X_3 @ B_65 ) ) ) ) )).

thf(fact_850_Int__def,axiom,(
    ! [A_110: ( pname > $o ) > $o,B_65: ( pname > $o ) > $o] :
      ( ( semila2013987940me_o_o @ A_110 @ B_65 )
      = ( collect_pname_o
        @ ^ [X_3: pname > $o] :
            ( (&) @ ( member_pname_o @ X_3 @ A_110 ) @ ( member_pname_o @ X_3 @ B_65 ) ) ) ) )).

thf(fact_851_Int__def,axiom,(
    ! [A_110: ( hoare_1708887482_state > $o ) > $o,B_65: ( hoare_1708887482_state > $o ) > $o] :
      ( ( semila598060698te_o_o @ A_110 @ B_65 )
      = ( collec219771562tate_o
        @ ^ [X_3: hoare_1708887482_state > $o] :
            ( (&) @ ( member814030440tate_o @ X_3 @ A_110 ) @ ( member814030440tate_o @ X_3 @ B_65 ) ) ) ) )).

thf(fact_852_set__diff__eq,axiom,(
    ! [A_109: com > $o,B_64: com > $o] :
      ( ( minus_minus_com_o @ A_109 @ B_64 )
      = ( collect_com
        @ ^ [X_3: com] :
            ( (&) @ ( member_com @ X_3 @ A_109 ) @ ( (~) @ ( member_com @ X_3 @ B_64 ) ) ) ) ) )).

thf(fact_853_set__diff__eq,axiom,(
    ! [A_109: pname > $o,B_64: pname > $o] :
      ( ( minus_minus_pname_o @ A_109 @ B_64 )
      = ( collect_pname
        @ ^ [X_3: pname] :
            ( (&) @ ( member_pname @ X_3 @ A_109 ) @ ( (~) @ ( member_pname @ X_3 @ B_64 ) ) ) ) ) )).

thf(fact_854_set__diff__eq,axiom,(
    ! [A_109: hoare_1708887482_state > $o,B_64: hoare_1708887482_state > $o] :
      ( ( minus_2056855718tate_o @ A_109 @ B_64 )
      = ( collec1568722789_state
        @ ^ [X_3: hoare_1708887482_state] :
            ( (&) @ ( member451959335_state @ X_3 @ A_109 ) @ ( (~) @ ( member451959335_state @ X_3 @ B_64 ) ) ) ) ) )).

thf(fact_855_set__diff__eq,axiom,(
    ! [A_109: ( pname > $o ) > $o,B_64: ( pname > $o ) > $o] :
      ( ( minus_1480864103me_o_o @ A_109 @ B_64 )
      = ( collect_pname_o
        @ ^ [X_3: pname > $o] :
            ( (&) @ ( member_pname_o @ X_3 @ A_109 ) @ ( (~) @ ( member_pname_o @ X_3 @ B_64 ) ) ) ) ) )).

thf(fact_856_set__diff__eq,axiom,(
    ! [A_109: ( hoare_1708887482_state > $o ) > $o,B_64: ( hoare_1708887482_state > $o ) > $o] :
      ( ( minus_548038231te_o_o @ A_109 @ B_64 )
      = ( collec219771562tate_o
        @ ^ [X_3: hoare_1708887482_state > $o] :
            ( (&) @ ( member814030440tate_o @ X_3 @ A_109 ) @ ( (~) @ ( member814030440tate_o @ X_3 @ B_64 ) ) ) ) ) )).

thf(fact_857_Int__Collect,axiom,(
    ! [X_44: com,A_108: com > $o,P_6: com > $o] :
      ( ( member_com @ X_44 @ ( semila513601829_com_o @ A_108 @ ( collect_com @ P_6 ) ) )
    <=> ( ( member_com @ X_44 @ A_108 )
        & ( P_6 @ X_44 ) ) ) )).

thf(fact_858_Int__Collect,axiom,(
    ! [X_44: pname,A_108: pname > $o,P_6: pname > $o] :
      ( ( member_pname @ X_44 @ ( semila1673364395name_o @ A_108 @ ( collect_pname @ P_6 ) ) )
    <=> ( ( member_pname @ X_44 @ A_108 )
        & ( P_6 @ X_44 ) ) ) )).

thf(fact_859_Int__Collect,axiom,(
    ! [X_44: hoare_1708887482_state,A_108: hoare_1708887482_state > $o,P_6: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ X_44 @ ( semila129691299tate_o @ A_108 @ ( collec1568722789_state @ P_6 ) ) )
    <=> ( ( member451959335_state @ X_44 @ A_108 )
        & ( P_6 @ X_44 ) ) ) )).

thf(fact_860_Int__Collect,axiom,(
    ! [X_44: pname > $o,A_108: ( pname > $o ) > $o,P_6: ( pname > $o ) > $o] :
      ( ( member_pname_o @ X_44 @ ( semila2013987940me_o_o @ A_108 @ ( collect_pname_o @ P_6 ) ) )
    <=> ( ( member_pname_o @ X_44 @ A_108 )
        & ( P_6 @ X_44 ) ) ) )).

thf(fact_861_Int__Collect,axiom,(
    ! [X_44: hoare_1708887482_state > $o,A_108: ( hoare_1708887482_state > $o ) > $o,P_6: ( hoare_1708887482_state > $o ) > $o] :
      ( ( member814030440tate_o @ X_44 @ ( semila598060698te_o_o @ A_108 @ ( collec219771562tate_o @ P_6 ) ) )
    <=> ( ( member814030440tate_o @ X_44 @ A_108 )
        & ( P_6 @ X_44 ) ) ) )).

thf(fact_862_Collect__conj__eq,axiom,(
    ! [P_5: hoare_1708887482_state > $o,Q_1: hoare_1708887482_state > $o] :
      ( ( collec1568722789_state
        @ ^ [X_3: hoare_1708887482_state] :
            ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
      = ( semila129691299tate_o @ ( collec1568722789_state @ P_5 ) @ ( collec1568722789_state @ Q_1 ) ) ) )).

thf(fact_863_Collect__conj__eq,axiom,(
    ! [P_5: pname > $o,Q_1: pname > $o] :
      ( ( collect_pname
        @ ^ [X_3: pname] :
            ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
      = ( semila1673364395name_o @ ( collect_pname @ P_5 ) @ ( collect_pname @ Q_1 ) ) ) )).

thf(fact_864_Collect__conj__eq,axiom,(
    ! [P_5: ( pname > $o ) > $o,Q_1: ( pname > $o ) > $o] :
      ( ( collect_pname_o
        @ ^ [X_3: pname > $o] :
            ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
      = ( semila2013987940me_o_o @ ( collect_pname_o @ P_5 ) @ ( collect_pname_o @ Q_1 ) ) ) )).

thf(fact_865_Collect__conj__eq,axiom,(
    ! [P_5: ( hoare_1708887482_state > $o ) > $o,Q_1: ( hoare_1708887482_state > $o ) > $o] :
      ( ( collec219771562tate_o
        @ ^ [X_3: hoare_1708887482_state > $o] :
            ( (&) @ ( P_5 @ X_3 ) @ ( Q_1 @ X_3 ) ) )
      = ( semila598060698te_o_o @ ( collec219771562tate_o @ P_5 ) @ ( collec219771562tate_o @ Q_1 ) ) ) )).

thf(fact_866_Diff__Int,axiom,(
    ! [A_107: pname > $o,B_63: pname > $o,C_21: pname > $o] :
      ( ( minus_minus_pname_o @ A_107 @ ( semila1673364395name_o @ B_63 @ C_21 ) )
      = ( semila1780557381name_o @ ( minus_minus_pname_o @ A_107 @ B_63 ) @ ( minus_minus_pname_o @ A_107 @ C_21 ) ) ) )).

thf(fact_867_Diff__Int,axiom,(
    ! [A_107: hoare_1708887482_state > $o,B_63: hoare_1708887482_state > $o,C_21: hoare_1708887482_state > $o] :
      ( ( minus_2056855718tate_o @ A_107 @ ( semila129691299tate_o @ B_63 @ C_21 ) )
      = ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A_107 @ B_63 ) @ ( minus_2056855718tate_o @ A_107 @ C_21 ) ) ) )).

thf(fact_868_Diff__Un,axiom,(
    ! [A_106: pname > $o,B_62: pname > $o,C_20: pname > $o] :
      ( ( minus_minus_pname_o @ A_106 @ ( semila1780557381name_o @ B_62 @ C_20 ) )
      = ( semila1673364395name_o @ ( minus_minus_pname_o @ A_106 @ B_62 ) @ ( minus_minus_pname_o @ A_106 @ C_20 ) ) ) )).

thf(fact_869_Diff__Un,axiom,(
    ! [A_106: hoare_1708887482_state > $o,B_62: hoare_1708887482_state > $o,C_20: hoare_1708887482_state > $o] :
      ( ( minus_2056855718tate_o @ A_106 @ ( semila1122118281tate_o @ B_62 @ C_20 ) )
      = ( semila129691299tate_o @ ( minus_2056855718tate_o @ A_106 @ B_62 ) @ ( minus_2056855718tate_o @ A_106 @ C_20 ) ) ) )).

thf(fact_870_Un__Diff__Int,axiom,(
    ! [A_105: pname > $o,B_61: pname > $o] :
      ( ( semila1780557381name_o @ ( minus_minus_pname_o @ A_105 @ B_61 ) @ ( semila1673364395name_o @ A_105 @ B_61 ) )
      = A_105 ) )).

thf(fact_871_Un__Diff__Int,axiom,(
    ! [A_105: hoare_1708887482_state > $o,B_61: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A_105 @ B_61 ) @ ( semila129691299tate_o @ A_105 @ B_61 ) )
      = A_105 ) )).

thf(fact_872_inf__sup__ord_I1_J,axiom,(
    ! [X_43: $o,Y_24: $o] :
      ( ord_less_eq_o @ ( semila854092349_inf_o @ X_43 @ Y_24 ) @ X_43 ) )).

thf(fact_873_inf__sup__ord_I1_J,axiom,(
    ! [X_43: pname > $o,Y_24: pname > $o] :
      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_43 @ Y_24 ) @ X_43 ) )).

thf(fact_874_inf__sup__ord_I1_J,axiom,(
    ! [X_43: hoare_1708887482_state > $o,Y_24: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_43 @ Y_24 ) @ X_43 ) )).

thf(fact_875_inf__le1,axiom,(
    ! [X_42: $o,Y_23: $o] :
      ( ord_less_eq_o @ ( semila854092349_inf_o @ X_42 @ Y_23 ) @ X_42 ) )).

thf(fact_876_inf__le1,axiom,(
    ! [X_42: pname > $o,Y_23: pname > $o] :
      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_42 @ Y_23 ) @ X_42 ) )).

thf(fact_877_inf__le1,axiom,(
    ! [X_42: hoare_1708887482_state > $o,Y_23: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_42 @ Y_23 ) @ X_42 ) )).

thf(fact_878_inf__sup__ord_I2_J,axiom,(
    ! [X_41: $o,Y_22: $o] :
      ( ord_less_eq_o @ ( semila854092349_inf_o @ X_41 @ Y_22 ) @ Y_22 ) )).

thf(fact_879_inf__sup__ord_I2_J,axiom,(
    ! [X_41: pname > $o,Y_22: pname > $o] :
      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_41 @ Y_22 ) @ Y_22 ) )).

thf(fact_880_inf__sup__ord_I2_J,axiom,(
    ! [X_41: hoare_1708887482_state > $o,Y_22: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_41 @ Y_22 ) @ Y_22 ) )).

thf(fact_881_inf__le2,axiom,(
    ! [X_40: $o,Y_21: $o] :
      ( ord_less_eq_o @ ( semila854092349_inf_o @ X_40 @ Y_21 ) @ Y_21 ) )).

thf(fact_882_inf__le2,axiom,(
    ! [X_40: pname > $o,Y_21: pname > $o] :
      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ X_40 @ Y_21 ) @ Y_21 ) )).

thf(fact_883_inf__le2,axiom,(
    ! [X_40: hoare_1708887482_state > $o,Y_21: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ ( semila129691299tate_o @ X_40 @ Y_21 ) @ Y_21 ) )).

thf(fact_884_le__iff__inf,axiom,(
    ! [X_39: $o,Y_20: $o] :
      ( ( ord_less_eq_o @ X_39 @ Y_20 )
    <=> ( ( semila854092349_inf_o @ X_39 @ Y_20 )
      <=> X_39 ) ) )).

thf(fact_885_le__iff__inf,axiom,(
    ! [X_39: pname > $o,Y_20: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_39 @ Y_20 )
    <=> ( ( semila1673364395name_o @ X_39 @ Y_20 )
        = X_39 ) ) )).

thf(fact_886_le__iff__inf,axiom,(
    ! [X_39: hoare_1708887482_state > $o,Y_20: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_39 @ Y_20 )
    <=> ( ( semila129691299tate_o @ X_39 @ Y_20 )
        = X_39 ) ) )).

thf(fact_887_le__inf__iff,axiom,(
    ! [X_38: $o,Y_19: $o,Z_10: $o] :
      ( ( ord_less_eq_o @ X_38 @ ( semila854092349_inf_o @ Y_19 @ Z_10 ) )
    <=> ( ( ord_less_eq_o @ X_38 @ Y_19 )
        & ( ord_less_eq_o @ X_38 @ Z_10 ) ) ) )).

thf(fact_888_le__inf__iff,axiom,(
    ! [X_38: pname > $o,Y_19: pname > $o,Z_10: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_38 @ ( semila1673364395name_o @ Y_19 @ Z_10 ) )
    <=> ( ( ord_less_eq_pname_o @ X_38 @ Y_19 )
        & ( ord_less_eq_pname_o @ X_38 @ Z_10 ) ) ) )).

thf(fact_889_le__inf__iff,axiom,(
    ! [X_38: hoare_1708887482_state > $o,Y_19: hoare_1708887482_state > $o,Z_10: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_38 @ ( semila129691299tate_o @ Y_19 @ Z_10 ) )
    <=> ( ( ord_le777019615tate_o @ X_38 @ Y_19 )
        & ( ord_le777019615tate_o @ X_38 @ Z_10 ) ) ) )).

thf(fact_890_le__infI1,axiom,(
    ! [B_60: $o,A_104: $o,X_37: $o] :
      ( ( ord_less_eq_o @ A_104 @ X_37 )
     => ( ord_less_eq_o @ ( semila854092349_inf_o @ A_104 @ B_60 ) @ X_37 ) ) )).

thf(fact_891_le__infI1,axiom,(
    ! [B_60: pname > $o,A_104: pname > $o,X_37: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_104 @ X_37 )
     => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_104 @ B_60 ) @ X_37 ) ) )).

thf(fact_892_le__infI1,axiom,(
    ! [B_60: hoare_1708887482_state > $o,A_104: hoare_1708887482_state > $o,X_37: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_104 @ X_37 )
     => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_104 @ B_60 ) @ X_37 ) ) )).

thf(fact_893_le__infI2,axiom,(
    ! [A_103: $o,B_59: $o,X_36: $o] :
      ( ( ord_less_eq_o @ B_59 @ X_36 )
     => ( ord_less_eq_o @ ( semila854092349_inf_o @ A_103 @ B_59 ) @ X_36 ) ) )).

thf(fact_894_le__infI2,axiom,(
    ! [A_103: pname > $o,B_59: pname > $o,X_36: pname > $o] :
      ( ( ord_less_eq_pname_o @ B_59 @ X_36 )
     => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_103 @ B_59 ) @ X_36 ) ) )).

thf(fact_895_le__infI2,axiom,(
    ! [A_103: hoare_1708887482_state > $o,B_59: hoare_1708887482_state > $o,X_36: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ B_59 @ X_36 )
     => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_103 @ B_59 ) @ X_36 ) ) )).

thf(fact_896_inf__absorb1,axiom,(
    ! [X_35: $o,Y_18: $o] :
      ( ( ord_less_eq_o @ X_35 @ Y_18 )
     => ( ( semila854092349_inf_o @ X_35 @ Y_18 )
      <=> X_35 ) ) )).

thf(fact_897_inf__absorb1,axiom,(
    ! [X_35: pname > $o,Y_18: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_35 @ Y_18 )
     => ( ( semila1673364395name_o @ X_35 @ Y_18 )
        = X_35 ) ) )).

thf(fact_898_inf__absorb1,axiom,(
    ! [X_35: hoare_1708887482_state > $o,Y_18: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_35 @ Y_18 )
     => ( ( semila129691299tate_o @ X_35 @ Y_18 )
        = X_35 ) ) )).

thf(fact_899_inf__absorb2,axiom,(
    ! [Y_17: $o,X_34: $o] :
      ( ( ord_less_eq_o @ Y_17 @ X_34 )
     => ( ( semila854092349_inf_o @ X_34 @ Y_17 )
      <=> Y_17 ) ) )).

thf(fact_900_inf__absorb2,axiom,(
    ! [Y_17: pname > $o,X_34: pname > $o] :
      ( ( ord_less_eq_pname_o @ Y_17 @ X_34 )
     => ( ( semila1673364395name_o @ X_34 @ Y_17 )
        = Y_17 ) ) )).

thf(fact_901_inf__absorb2,axiom,(
    ! [Y_17: hoare_1708887482_state > $o,X_34: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ Y_17 @ X_34 )
     => ( ( semila129691299tate_o @ X_34 @ Y_17 )
        = Y_17 ) ) )).

thf(fact_902_le__infI,axiom,(
    ! [B_58: $o,X_33: $o,A_102: $o] :
      ( ( ord_less_eq_o @ X_33 @ A_102 )
     => ( ( ord_less_eq_o @ X_33 @ B_58 )
       => ( ord_less_eq_o @ X_33 @ ( semila854092349_inf_o @ A_102 @ B_58 ) ) ) ) )).

thf(fact_903_le__infI,axiom,(
    ! [B_58: pname > $o,X_33: pname > $o,A_102: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_33 @ A_102 )
     => ( ( ord_less_eq_pname_o @ X_33 @ B_58 )
       => ( ord_less_eq_pname_o @ X_33 @ ( semila1673364395name_o @ A_102 @ B_58 ) ) ) ) )).

thf(fact_904_le__infI,axiom,(
    ! [B_58: hoare_1708887482_state > $o,X_33: hoare_1708887482_state > $o,A_102: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_33 @ A_102 )
     => ( ( ord_le777019615tate_o @ X_33 @ B_58 )
       => ( ord_le777019615tate_o @ X_33 @ ( semila129691299tate_o @ A_102 @ B_58 ) ) ) ) )).

thf(fact_905_inf__greatest,axiom,(
    ! [Z_9: $o,X_32: $o,Y_16: $o] :
      ( ( ord_less_eq_o @ X_32 @ Y_16 )
     => ( ( ord_less_eq_o @ X_32 @ Z_9 )
       => ( ord_less_eq_o @ X_32 @ ( semila854092349_inf_o @ Y_16 @ Z_9 ) ) ) ) )).

thf(fact_906_inf__greatest,axiom,(
    ! [Z_9: pname > $o,X_32: pname > $o,Y_16: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_32 @ Y_16 )
     => ( ( ord_less_eq_pname_o @ X_32 @ Z_9 )
       => ( ord_less_eq_pname_o @ X_32 @ ( semila1673364395name_o @ Y_16 @ Z_9 ) ) ) ) )).

thf(fact_907_inf__greatest,axiom,(
    ! [Z_9: hoare_1708887482_state > $o,X_32: hoare_1708887482_state > $o,Y_16: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_32 @ Y_16 )
     => ( ( ord_le777019615tate_o @ X_32 @ Z_9 )
       => ( ord_le777019615tate_o @ X_32 @ ( semila129691299tate_o @ Y_16 @ Z_9 ) ) ) ) )).

thf(fact_908_inf__mono,axiom,(
    ! [B_57: $o,D_2: $o,A_101: $o,C_19: $o] :
      ( ( ord_less_eq_o @ A_101 @ C_19 )
     => ( ( ord_less_eq_o @ B_57 @ D_2 )
       => ( ord_less_eq_o @ ( semila854092349_inf_o @ A_101 @ B_57 ) @ ( semila854092349_inf_o @ C_19 @ D_2 ) ) ) ) )).

thf(fact_909_inf__mono,axiom,(
    ! [B_57: pname > $o,D_2: pname > $o,A_101: pname > $o,C_19: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_101 @ C_19 )
     => ( ( ord_less_eq_pname_o @ B_57 @ D_2 )
       => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_101 @ B_57 ) @ ( semila1673364395name_o @ C_19 @ D_2 ) ) ) ) )).

thf(fact_910_inf__mono,axiom,(
    ! [B_57: hoare_1708887482_state > $o,D_2: hoare_1708887482_state > $o,A_101: hoare_1708887482_state > $o,C_19: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_101 @ C_19 )
     => ( ( ord_le777019615tate_o @ B_57 @ D_2 )
       => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_101 @ B_57 ) @ ( semila129691299tate_o @ C_19 @ D_2 ) ) ) ) )).

thf(fact_911_le__infE,axiom,(
    ! [X_31: $o,A_100: $o,B_56: $o] :
      ( ( ord_less_eq_o @ X_31 @ ( semila854092349_inf_o @ A_100 @ B_56 ) )
     => ~ ( ( ord_less_eq_o @ X_31 @ A_100 )
         => ~ ( ord_less_eq_o @ X_31 @ B_56 ) ) ) )).

thf(fact_912_le__infE,axiom,(
    ! [X_31: pname > $o,A_100: pname > $o,B_56: pname > $o] :
      ( ( ord_less_eq_pname_o @ X_31 @ ( semila1673364395name_o @ A_100 @ B_56 ) )
     => ~ ( ( ord_less_eq_pname_o @ X_31 @ A_100 )
         => ~ ( ord_less_eq_pname_o @ X_31 @ B_56 ) ) ) )).

thf(fact_913_le__infE,axiom,(
    ! [X_31: hoare_1708887482_state > $o,A_100: hoare_1708887482_state > $o,B_56: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ X_31 @ ( semila129691299tate_o @ A_100 @ B_56 ) )
     => ~ ( ( ord_le777019615tate_o @ X_31 @ A_100 )
         => ~ ( ord_le777019615tate_o @ X_31 @ B_56 ) ) ) )).

thf(fact_914_inf__bot__right,axiom,(
    ! [X_30: com > $o] :
      ( ( semila513601829_com_o @ X_30 @ bot_bot_com_o )
      = bot_bot_com_o ) )).

thf(fact_915_inf__bot__right,axiom,(
    ! [X_30: $o] :
      ( ( semila854092349_inf_o @ X_30 @ bot_bot_o )
    <=> bot_bot_o ) )).

thf(fact_916_inf__bot__right,axiom,(
    ! [X_30: pname > $o] :
      ( ( semila1673364395name_o @ X_30 @ bot_bot_pname_o )
      = bot_bot_pname_o ) )).

thf(fact_917_inf__bot__right,axiom,(
    ! [X_30: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ X_30 @ bot_bo19817387tate_o )
      = bot_bo19817387tate_o ) )).

thf(fact_918_inf__bot__left,axiom,(
    ! [X_29: com > $o] :
      ( ( semila513601829_com_o @ bot_bot_com_o @ X_29 )
      = bot_bot_com_o ) )).

thf(fact_919_inf__bot__left,axiom,(
    ! [X_29: $o] :
      ( ( semila854092349_inf_o @ bot_bot_o @ X_29 )
    <=> bot_bot_o ) )).

thf(fact_920_inf__bot__left,axiom,(
    ! [X_29: pname > $o] :
      ( ( semila1673364395name_o @ bot_bot_pname_o @ X_29 )
      = bot_bot_pname_o ) )).

thf(fact_921_inf__bot__left,axiom,(
    ! [X_29: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ bot_bo19817387tate_o @ X_29 )
      = bot_bo19817387tate_o ) )).

thf(fact_922_inf__sup__absorb,axiom,(
    ! [X_28: $o,Y_15: $o] :
      ( ( semila854092349_inf_o @ X_28 @ ( semila10642723_sup_o @ X_28 @ Y_15 ) )
    <=> X_28 ) )).

thf(fact_923_inf__sup__absorb,axiom,(
    ! [X_28: pname > $o,Y_15: pname > $o] :
      ( ( semila1673364395name_o @ X_28 @ ( semila1780557381name_o @ X_28 @ Y_15 ) )
      = X_28 ) )).

thf(fact_924_inf__sup__absorb,axiom,(
    ! [X_28: hoare_1708887482_state > $o,Y_15: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ X_28 @ ( semila1122118281tate_o @ X_28 @ Y_15 ) )
      = X_28 ) )).

thf(fact_925_sup__inf__absorb,axiom,(
    ! [X_27: $o,Y_14: $o] :
      ( ( semila10642723_sup_o @ X_27 @ ( semila854092349_inf_o @ X_27 @ Y_14 ) )
    <=> X_27 ) )).

thf(fact_926_sup__inf__absorb,axiom,(
    ! [X_27: pname > $o,Y_14: pname > $o] :
      ( ( semila1780557381name_o @ X_27 @ ( semila1673364395name_o @ X_27 @ Y_14 ) )
      = X_27 ) )).

thf(fact_927_sup__inf__absorb,axiom,(
    ! [X_27: hoare_1708887482_state > $o,Y_14: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ X_27 @ ( semila129691299tate_o @ X_27 @ Y_14 ) )
      = X_27 ) )).

thf(fact_928_inf__sup__distrib1,axiom,(
    ! [X_26: $o,Y_13: $o,Z_8: $o] :
      ( ( semila854092349_inf_o @ X_26 @ ( semila10642723_sup_o @ Y_13 @ Z_8 ) )
    <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_26 @ Y_13 ) @ ( semila854092349_inf_o @ X_26 @ Z_8 ) ) ) )).

thf(fact_929_inf__sup__distrib1,axiom,(
    ! [X_26: pname > $o,Y_13: pname > $o,Z_8: pname > $o] :
      ( ( semila1673364395name_o @ X_26 @ ( semila1780557381name_o @ Y_13 @ Z_8 ) )
      = ( semila1780557381name_o @ ( semila1673364395name_o @ X_26 @ Y_13 ) @ ( semila1673364395name_o @ X_26 @ Z_8 ) ) ) )).

thf(fact_930_inf__sup__distrib1,axiom,(
    ! [X_26: hoare_1708887482_state > $o,Y_13: hoare_1708887482_state > $o,Z_8: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ X_26 @ ( semila1122118281tate_o @ Y_13 @ Z_8 ) )
      = ( semila1122118281tate_o @ ( semila129691299tate_o @ X_26 @ Y_13 ) @ ( semila129691299tate_o @ X_26 @ Z_8 ) ) ) )).

thf(fact_931_sup__inf__distrib1,axiom,(
    ! [X_25: $o,Y_12: $o,Z_7: $o] :
      ( ( semila10642723_sup_o @ X_25 @ ( semila854092349_inf_o @ Y_12 @ Z_7 ) )
    <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_25 @ Y_12 ) @ ( semila10642723_sup_o @ X_25 @ Z_7 ) ) ) )).

thf(fact_932_sup__inf__distrib1,axiom,(
    ! [X_25: pname > $o,Y_12: pname > $o,Z_7: pname > $o] :
      ( ( semila1780557381name_o @ X_25 @ ( semila1673364395name_o @ Y_12 @ Z_7 ) )
      = ( semila1673364395name_o @ ( semila1780557381name_o @ X_25 @ Y_12 ) @ ( semila1780557381name_o @ X_25 @ Z_7 ) ) ) )).

thf(fact_933_sup__inf__distrib1,axiom,(
    ! [X_25: hoare_1708887482_state > $o,Y_12: hoare_1708887482_state > $o,Z_7: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ X_25 @ ( semila129691299tate_o @ Y_12 @ Z_7 ) )
      = ( semila129691299tate_o @ ( semila1122118281tate_o @ X_25 @ Y_12 ) @ ( semila1122118281tate_o @ X_25 @ Z_7 ) ) ) )).

thf(fact_934_inf__sup__distrib2,axiom,(
    ! [Y_11: $o,Z_6: $o,X_24: $o] :
      ( ( semila854092349_inf_o @ ( semila10642723_sup_o @ Y_11 @ Z_6 ) @ X_24 )
    <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ Y_11 @ X_24 ) @ ( semila854092349_inf_o @ Z_6 @ X_24 ) ) ) )).

thf(fact_935_inf__sup__distrib2,axiom,(
    ! [Y_11: pname > $o,Z_6: pname > $o,X_24: pname > $o] :
      ( ( semila1673364395name_o @ ( semila1780557381name_o @ Y_11 @ Z_6 ) @ X_24 )
      = ( semila1780557381name_o @ ( semila1673364395name_o @ Y_11 @ X_24 ) @ ( semila1673364395name_o @ Z_6 @ X_24 ) ) ) )).

thf(fact_936_inf__sup__distrib2,axiom,(
    ! [Y_11: hoare_1708887482_state > $o,Z_6: hoare_1708887482_state > $o,X_24: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ ( semila1122118281tate_o @ Y_11 @ Z_6 ) @ X_24 )
      = ( semila1122118281tate_o @ ( semila129691299tate_o @ Y_11 @ X_24 ) @ ( semila129691299tate_o @ Z_6 @ X_24 ) ) ) )).

thf(fact_937_sup__inf__distrib2,axiom,(
    ! [Y_10: $o,Z_5: $o,X_23: $o] :
      ( ( semila10642723_sup_o @ ( semila854092349_inf_o @ Y_10 @ Z_5 ) @ X_23 )
    <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ Y_10 @ X_23 ) @ ( semila10642723_sup_o @ Z_5 @ X_23 ) ) ) )).

thf(fact_938_sup__inf__distrib2,axiom,(
    ! [Y_10: pname > $o,Z_5: pname > $o,X_23: pname > $o] :
      ( ( semila1780557381name_o @ ( semila1673364395name_o @ Y_10 @ Z_5 ) @ X_23 )
      = ( semila1673364395name_o @ ( semila1780557381name_o @ Y_10 @ X_23 ) @ ( semila1780557381name_o @ Z_5 @ X_23 ) ) ) )).

thf(fact_939_sup__inf__distrib2,axiom,(
    ! [Y_10: hoare_1708887482_state > $o,Z_5: hoare_1708887482_state > $o,X_23: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ ( semila129691299tate_o @ Y_10 @ Z_5 ) @ X_23 )
      = ( semila129691299tate_o @ ( semila1122118281tate_o @ Y_10 @ X_23 ) @ ( semila1122118281tate_o @ Z_5 @ X_23 ) ) ) )).

thf(fact_940_Diff__cancel,axiom,(
    ! [A_99: com > $o] :
      ( ( minus_minus_com_o @ A_99 @ A_99 )
      = bot_bot_com_o ) )).

thf(fact_941_Diff__cancel,axiom,(
    ! [A_99: pname > $o] :
      ( ( minus_minus_pname_o @ A_99 @ A_99 )
      = bot_bot_pname_o ) )).

thf(fact_942_Diff__cancel,axiom,(
    ! [A_99: hoare_1708887482_state > $o] :
      ( ( minus_2056855718tate_o @ A_99 @ A_99 )
      = bot_bo19817387tate_o ) )).

thf(fact_943_Diff__empty,axiom,(
    ! [A_98: com > $o] :
      ( ( minus_minus_com_o @ A_98 @ bot_bot_com_o )
      = A_98 ) )).

thf(fact_944_Diff__empty,axiom,(
    ! [A_98: pname > $o] :
      ( ( minus_minus_pname_o @ A_98 @ bot_bot_pname_o )
      = A_98 ) )).

thf(fact_945_Diff__empty,axiom,(
    ! [A_98: hoare_1708887482_state > $o] :
      ( ( minus_2056855718tate_o @ A_98 @ bot_bo19817387tate_o )
      = A_98 ) )).

thf(fact_946_empty__Diff,axiom,(
    ! [A_97: com > $o] :
      ( ( minus_minus_com_o @ bot_bot_com_o @ A_97 )
      = bot_bot_com_o ) )).

thf(fact_947_empty__Diff,axiom,(
    ! [A_97: pname > $o] :
      ( ( minus_minus_pname_o @ bot_bot_pname_o @ A_97 )
      = bot_bot_pname_o ) )).

thf(fact_948_empty__Diff,axiom,(
    ! [A_97: hoare_1708887482_state > $o] :
      ( ( minus_2056855718tate_o @ bot_bo19817387tate_o @ A_97 )
      = bot_bo19817387tate_o ) )).

thf(fact_949_finite__Diff2,axiom,(
    ! [A_96: ( pname > $o ) > $o,B_55: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ B_55 )
     => ( ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_96 @ B_55 ) )
      <=> ( finite297249702name_o @ A_96 ) ) ) )).

thf(fact_950_finite__Diff2,axiom,(
    ! [A_96: ( hoare_1708887482_state > $o ) > $o,B_55: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ B_55 )
     => ( ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_96 @ B_55 ) )
      <=> ( finite1329924456tate_o @ A_96 ) ) ) )).

thf(fact_951_finite__Diff2,axiom,(
    ! [A_96: pname > $o,B_55: pname > $o] :
      ( ( finite_finite_pname @ B_55 )
     => ( ( finite_finite_pname @ ( minus_minus_pname_o @ A_96 @ B_55 ) )
      <=> ( finite_finite_pname @ A_96 ) ) ) )).

thf(fact_952_finite__Diff2,axiom,(
    ! [A_96: hoare_1708887482_state > $o,B_55: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ B_55 )
     => ( ( finite1625599783_state @ ( minus_2056855718tate_o @ A_96 @ B_55 ) )
      <=> ( finite1625599783_state @ A_96 ) ) ) )).

thf(fact_953_insert__Diff1,axiom,(
    ! [A_95: com > $o,X_22: com,B_54: com > $o] :
      ( ( member_com @ X_22 @ B_54 )
     => ( ( minus_minus_com_o @ ( insert_com @ X_22 @ A_95 ) @ B_54 )
        = ( minus_minus_com_o @ A_95 @ B_54 ) ) ) )).

thf(fact_954_insert__Diff1,axiom,(
    ! [A_95: pname > $o,X_22: pname,B_54: pname > $o] :
      ( ( member_pname @ X_22 @ B_54 )
     => ( ( minus_minus_pname_o @ ( insert_pname @ X_22 @ A_95 ) @ B_54 )
        = ( minus_minus_pname_o @ A_95 @ B_54 ) ) ) )).

thf(fact_955_insert__Diff1,axiom,(
    ! [A_95: hoare_1708887482_state > $o,X_22: hoare_1708887482_state,B_54: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ X_22 @ B_54 )
     => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_22 @ A_95 ) @ B_54 )
        = ( minus_2056855718tate_o @ A_95 @ B_54 ) ) ) )).

thf(fact_956_insert__Diff__if,axiom,(
    ! [A_94: com > $o,X_21: com,B_53: com > $o] :
      ( ( ( member_com @ X_21 @ B_53 )
       => ( ( minus_minus_com_o @ ( insert_com @ X_21 @ A_94 ) @ B_53 )
          = ( minus_minus_com_o @ A_94 @ B_53 ) ) )
      & ( ~ ( member_com @ X_21 @ B_53 )
       => ( ( minus_minus_com_o @ ( insert_com @ X_21 @ A_94 ) @ B_53 )
          = ( insert_com @ X_21 @ ( minus_minus_com_o @ A_94 @ B_53 ) ) ) ) ) )).

thf(fact_957_insert__Diff__if,axiom,(
    ! [A_94: pname > $o,X_21: pname,B_53: pname > $o] :
      ( ( ( member_pname @ X_21 @ B_53 )
       => ( ( minus_minus_pname_o @ ( insert_pname @ X_21 @ A_94 ) @ B_53 )
          = ( minus_minus_pname_o @ A_94 @ B_53 ) ) )
      & ( ~ ( member_pname @ X_21 @ B_53 )
       => ( ( minus_minus_pname_o @ ( insert_pname @ X_21 @ A_94 ) @ B_53 )
          = ( insert_pname @ X_21 @ ( minus_minus_pname_o @ A_94 @ B_53 ) ) ) ) ) )).

thf(fact_958_insert__Diff__if,axiom,(
    ! [A_94: hoare_1708887482_state > $o,X_21: hoare_1708887482_state,B_53: hoare_1708887482_state > $o] :
      ( ( ( member451959335_state @ X_21 @ B_53 )
       => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_21 @ A_94 ) @ B_53 )
          = ( minus_2056855718tate_o @ A_94 @ B_53 ) ) )
      & ( ~ ( member451959335_state @ X_21 @ B_53 )
       => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_21 @ A_94 ) @ B_53 )
          = ( insert528405184_state @ X_21 @ ( minus_2056855718tate_o @ A_94 @ B_53 ) ) ) ) ) )).

thf(fact_959_disjoint__iff__not__equal,axiom,(
    ! [A_93: com > $o,B_52: com > $o] :
      ( ( ( semila513601829_com_o @ A_93 @ B_52 )
        = bot_bot_com_o )
    <=> ! [X_3: com] :
          ( ( member_com @ X_3 @ A_93 )
         => ! [Xa: com] :
              ( ( member_com @ Xa @ B_52 )
             => ( X_3 != Xa ) ) ) ) )).

thf(fact_960_disjoint__iff__not__equal,axiom,(
    ! [A_93: pname > $o,B_52: pname > $o] :
      ( ( ( semila1673364395name_o @ A_93 @ B_52 )
        = bot_bot_pname_o )
    <=> ! [X_3: pname] :
          ( ( member_pname @ X_3 @ A_93 )
         => ! [Xa: pname] :
              ( ( member_pname @ Xa @ B_52 )
             => ( X_3 != Xa ) ) ) ) )).

thf(fact_961_disjoint__iff__not__equal,axiom,(
    ! [A_93: hoare_1708887482_state > $o,B_52: hoare_1708887482_state > $o] :
      ( ( ( semila129691299tate_o @ A_93 @ B_52 )
        = bot_bo19817387tate_o )
    <=> ! [X_3: hoare_1708887482_state] :
          ( ( member451959335_state @ X_3 @ A_93 )
         => ! [Xa: hoare_1708887482_state] :
              ( ( member451959335_state @ Xa @ B_52 )
             => ( X_3 != Xa ) ) ) ) )).

thf(fact_962_Int__empty__right,axiom,(
    ! [A_92: com > $o] :
      ( ( semila513601829_com_o @ A_92 @ bot_bot_com_o )
      = bot_bot_com_o ) )).

thf(fact_963_Int__empty__right,axiom,(
    ! [A_92: pname > $o] :
      ( ( semila1673364395name_o @ A_92 @ bot_bot_pname_o )
      = bot_bot_pname_o ) )).

thf(fact_964_Int__empty__right,axiom,(
    ! [A_92: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ A_92 @ bot_bo19817387tate_o )
      = bot_bo19817387tate_o ) )).

thf(fact_965_Int__empty__left,axiom,(
    ! [B_51: com > $o] :
      ( ( semila513601829_com_o @ bot_bot_com_o @ B_51 )
      = bot_bot_com_o ) )).

thf(fact_966_Int__empty__left,axiom,(
    ! [B_51: pname > $o] :
      ( ( semila1673364395name_o @ bot_bot_pname_o @ B_51 )
      = bot_bot_pname_o ) )).

thf(fact_967_Int__empty__left,axiom,(
    ! [B_51: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ bot_bo19817387tate_o @ B_51 )
      = bot_bo19817387tate_o ) )).

thf(fact_968_double__diff,axiom,(
    ! [C_18: pname > $o,A_91: pname > $o,B_50: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_91 @ B_50 )
     => ( ( ord_less_eq_pname_o @ B_50 @ C_18 )
       => ( ( minus_minus_pname_o @ B_50 @ ( minus_minus_pname_o @ C_18 @ A_91 ) )
          = A_91 ) ) ) )).

thf(fact_969_double__diff,axiom,(
    ! [C_18: hoare_1708887482_state > $o,A_91: hoare_1708887482_state > $o,B_50: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_91 @ B_50 )
     => ( ( ord_le777019615tate_o @ B_50 @ C_18 )
       => ( ( minus_2056855718tate_o @ B_50 @ ( minus_2056855718tate_o @ C_18 @ A_91 ) )
          = A_91 ) ) ) )).

thf(fact_970_Diff__mono,axiom,(
    ! [D_1: pname > $o,B_49: pname > $o,A_90: pname > $o,C_17: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_90 @ C_17 )
     => ( ( ord_less_eq_pname_o @ D_1 @ B_49 )
       => ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_90 @ B_49 ) @ ( minus_minus_pname_o @ C_17 @ D_1 ) ) ) ) )).

thf(fact_971_Diff__mono,axiom,(
    ! [D_1: hoare_1708887482_state > $o,B_49: hoare_1708887482_state > $o,A_90: hoare_1708887482_state > $o,C_17: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_90 @ C_17 )
     => ( ( ord_le777019615tate_o @ D_1 @ B_49 )
       => ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_90 @ B_49 ) @ ( minus_2056855718tate_o @ C_17 @ D_1 ) ) ) ) )).

thf(fact_972_Diff__subset,axiom,(
    ! [A_89: pname > $o,B_48: pname > $o] :
      ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_89 @ B_48 ) @ A_89 ) )).

thf(fact_973_Diff__subset,axiom,(
    ! [A_89: hoare_1708887482_state > $o,B_48: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_89 @ B_48 ) @ A_89 ) )).

thf(fact_974_Un__Diff,axiom,(
    ! [A_88: pname > $o,B_47: pname > $o,C_16: pname > $o] :
      ( ( minus_minus_pname_o @ ( semila1780557381name_o @ A_88 @ B_47 ) @ C_16 )
      = ( semila1780557381name_o @ ( minus_minus_pname_o @ A_88 @ C_16 ) @ ( minus_minus_pname_o @ B_47 @ C_16 ) ) ) )).

thf(fact_975_Un__Diff,axiom,(
    ! [A_88: hoare_1708887482_state > $o,B_47: hoare_1708887482_state > $o,C_16: hoare_1708887482_state > $o] :
      ( ( minus_2056855718tate_o @ ( semila1122118281tate_o @ A_88 @ B_47 ) @ C_16 )
      = ( semila1122118281tate_o @ ( minus_2056855718tate_o @ A_88 @ C_16 ) @ ( minus_2056855718tate_o @ B_47 @ C_16 ) ) ) )).

thf(fact_976_Un__Diff__cancel2,axiom,(
    ! [B_46: pname > $o,A_87: pname > $o] :
      ( ( semila1780557381name_o @ ( minus_minus_pname_o @ B_46 @ A_87 ) @ A_87 )
      = ( semila1780557381name_o @ B_46 @ A_87 ) ) )).

thf(fact_977_Un__Diff__cancel2,axiom,(
    ! [B_46: hoare_1708887482_state > $o,A_87: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ ( minus_2056855718tate_o @ B_46 @ A_87 ) @ A_87 )
      = ( semila1122118281tate_o @ B_46 @ A_87 ) ) )).

thf(fact_978_Un__Diff__cancel,axiom,(
    ! [A_86: pname > $o,B_45: pname > $o] :
      ( ( semila1780557381name_o @ A_86 @ ( minus_minus_pname_o @ B_45 @ A_86 ) )
      = ( semila1780557381name_o @ A_86 @ B_45 ) ) )).

thf(fact_979_Un__Diff__cancel,axiom,(
    ! [A_86: hoare_1708887482_state > $o,B_45: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_86 @ ( minus_2056855718tate_o @ B_45 @ A_86 ) )
      = ( semila1122118281tate_o @ A_86 @ B_45 ) ) )).

thf(fact_980_Int__insert__left__if1,axiom,(
    ! [B_44: com > $o,A_85: com,C_15: com > $o] :
      ( ( member_com @ A_85 @ C_15 )
     => ( ( semila513601829_com_o @ ( insert_com @ A_85 @ B_44 ) @ C_15 )
        = ( insert_com @ A_85 @ ( semila513601829_com_o @ B_44 @ C_15 ) ) ) ) )).

thf(fact_981_Int__insert__left__if1,axiom,(
    ! [B_44: pname > $o,A_85: pname,C_15: pname > $o] :
      ( ( member_pname @ A_85 @ C_15 )
     => ( ( semila1673364395name_o @ ( insert_pname @ A_85 @ B_44 ) @ C_15 )
        = ( insert_pname @ A_85 @ ( semila1673364395name_o @ B_44 @ C_15 ) ) ) ) )).

thf(fact_982_Int__insert__left__if1,axiom,(
    ! [B_44: hoare_1708887482_state > $o,A_85: hoare_1708887482_state,C_15: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ A_85 @ C_15 )
     => ( ( semila129691299tate_o @ ( insert528405184_state @ A_85 @ B_44 ) @ C_15 )
        = ( insert528405184_state @ A_85 @ ( semila129691299tate_o @ B_44 @ C_15 ) ) ) ) )).

thf(fact_983_Int__insert__right__if1,axiom,(
    ! [B_43: com > $o,A_84: com,A_83: com > $o] :
      ( ( member_com @ A_84 @ A_83 )
     => ( ( semila513601829_com_o @ A_83 @ ( insert_com @ A_84 @ B_43 ) )
        = ( insert_com @ A_84 @ ( semila513601829_com_o @ A_83 @ B_43 ) ) ) ) )).

thf(fact_984_Int__insert__right__if1,axiom,(
    ! [B_43: pname > $o,A_84: pname,A_83: pname > $o] :
      ( ( member_pname @ A_84 @ A_83 )
     => ( ( semila1673364395name_o @ A_83 @ ( insert_pname @ A_84 @ B_43 ) )
        = ( insert_pname @ A_84 @ ( semila1673364395name_o @ A_83 @ B_43 ) ) ) ) )).

thf(fact_985_Int__insert__right__if1,axiom,(
    ! [B_43: hoare_1708887482_state > $o,A_84: hoare_1708887482_state,A_83: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ A_84 @ A_83 )
     => ( ( semila129691299tate_o @ A_83 @ ( insert528405184_state @ A_84 @ B_43 ) )
        = ( insert528405184_state @ A_84 @ ( semila129691299tate_o @ A_83 @ B_43 ) ) ) ) )).

thf(fact_986_Int__insert__left__if0,axiom,(
    ! [B_42: com > $o,A_82: com,C_14: com > $o] :
      ( ~ ( member_com @ A_82 @ C_14 )
     => ( ( semila513601829_com_o @ ( insert_com @ A_82 @ B_42 ) @ C_14 )
        = ( semila513601829_com_o @ B_42 @ C_14 ) ) ) )).

thf(fact_987_Int__insert__left__if0,axiom,(
    ! [B_42: pname > $o,A_82: pname,C_14: pname > $o] :
      ( ~ ( member_pname @ A_82 @ C_14 )
     => ( ( semila1673364395name_o @ ( insert_pname @ A_82 @ B_42 ) @ C_14 )
        = ( semila1673364395name_o @ B_42 @ C_14 ) ) ) )).

thf(fact_988_Int__insert__left__if0,axiom,(
    ! [B_42: hoare_1708887482_state > $o,A_82: hoare_1708887482_state,C_14: hoare_1708887482_state > $o] :
      ( ~ ( member451959335_state @ A_82 @ C_14 )
     => ( ( semila129691299tate_o @ ( insert528405184_state @ A_82 @ B_42 ) @ C_14 )
        = ( semila129691299tate_o @ B_42 @ C_14 ) ) ) )).

thf(fact_989_Int__insert__right__if0,axiom,(
    ! [B_41: com > $o,A_81: com,A_80: com > $o] :
      ( ~ ( member_com @ A_81 @ A_80 )
     => ( ( semila513601829_com_o @ A_80 @ ( insert_com @ A_81 @ B_41 ) )
        = ( semila513601829_com_o @ A_80 @ B_41 ) ) ) )).

thf(fact_990_Int__insert__right__if0,axiom,(
    ! [B_41: pname > $o,A_81: pname,A_80: pname > $o] :
      ( ~ ( member_pname @ A_81 @ A_80 )
     => ( ( semila1673364395name_o @ A_80 @ ( insert_pname @ A_81 @ B_41 ) )
        = ( semila1673364395name_o @ A_80 @ B_41 ) ) ) )).

thf(fact_991_Int__insert__right__if0,axiom,(
    ! [B_41: hoare_1708887482_state > $o,A_81: hoare_1708887482_state,A_80: hoare_1708887482_state > $o] :
      ( ~ ( member451959335_state @ A_81 @ A_80 )
     => ( ( semila129691299tate_o @ A_80 @ ( insert528405184_state @ A_81 @ B_41 ) )
        = ( semila129691299tate_o @ A_80 @ B_41 ) ) ) )).

thf(fact_992_insert__inter__insert,axiom,(
    ! [A_79: com,A_78: com > $o,B_40: com > $o] :
      ( ( semila513601829_com_o @ ( insert_com @ A_79 @ A_78 ) @ ( insert_com @ A_79 @ B_40 ) )
      = ( insert_com @ A_79 @ ( semila513601829_com_o @ A_78 @ B_40 ) ) ) )).

thf(fact_993_insert__inter__insert,axiom,(
    ! [A_79: pname,A_78: pname > $o,B_40: pname > $o] :
      ( ( semila1673364395name_o @ ( insert_pname @ A_79 @ A_78 ) @ ( insert_pname @ A_79 @ B_40 ) )
      = ( insert_pname @ A_79 @ ( semila1673364395name_o @ A_78 @ B_40 ) ) ) )).

thf(fact_994_insert__inter__insert,axiom,(
    ! [A_79: hoare_1708887482_state,A_78: hoare_1708887482_state > $o,B_40: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ ( insert528405184_state @ A_79 @ A_78 ) @ ( insert528405184_state @ A_79 @ B_40 ) )
      = ( insert528405184_state @ A_79 @ ( semila129691299tate_o @ A_78 @ B_40 ) ) ) )).

thf(fact_995_Int__insert__left,axiom,(
    ! [B_39: com > $o,A_77: com,C_13: com > $o] :
      ( ( ( member_com @ A_77 @ C_13 )
       => ( ( semila513601829_com_o @ ( insert_com @ A_77 @ B_39 ) @ C_13 )
          = ( insert_com @ A_77 @ ( semila513601829_com_o @ B_39 @ C_13 ) ) ) )
      & ( ~ ( member_com @ A_77 @ C_13 )
       => ( ( semila513601829_com_o @ ( insert_com @ A_77 @ B_39 ) @ C_13 )
          = ( semila513601829_com_o @ B_39 @ C_13 ) ) ) ) )).

thf(fact_996_Int__insert__left,axiom,(
    ! [B_39: pname > $o,A_77: pname,C_13: pname > $o] :
      ( ( ( member_pname @ A_77 @ C_13 )
       => ( ( semila1673364395name_o @ ( insert_pname @ A_77 @ B_39 ) @ C_13 )
          = ( insert_pname @ A_77 @ ( semila1673364395name_o @ B_39 @ C_13 ) ) ) )
      & ( ~ ( member_pname @ A_77 @ C_13 )
       => ( ( semila1673364395name_o @ ( insert_pname @ A_77 @ B_39 ) @ C_13 )
          = ( semila1673364395name_o @ B_39 @ C_13 ) ) ) ) )).

thf(fact_997_Int__insert__left,axiom,(
    ! [B_39: hoare_1708887482_state > $o,A_77: hoare_1708887482_state,C_13: hoare_1708887482_state > $o] :
      ( ( ( member451959335_state @ A_77 @ C_13 )
       => ( ( semila129691299tate_o @ ( insert528405184_state @ A_77 @ B_39 ) @ C_13 )
          = ( insert528405184_state @ A_77 @ ( semila129691299tate_o @ B_39 @ C_13 ) ) ) )
      & ( ~ ( member451959335_state @ A_77 @ C_13 )
       => ( ( semila129691299tate_o @ ( insert528405184_state @ A_77 @ B_39 ) @ C_13 )
          = ( semila129691299tate_o @ B_39 @ C_13 ) ) ) ) )).

thf(fact_998_Int__insert__right,axiom,(
    ! [B_38: com > $o,A_76: com,A_75: com > $o] :
      ( ( ( member_com @ A_76 @ A_75 )
       => ( ( semila513601829_com_o @ A_75 @ ( insert_com @ A_76 @ B_38 ) )
          = ( insert_com @ A_76 @ ( semila513601829_com_o @ A_75 @ B_38 ) ) ) )
      & ( ~ ( member_com @ A_76 @ A_75 )
       => ( ( semila513601829_com_o @ A_75 @ ( insert_com @ A_76 @ B_38 ) )
          = ( semila513601829_com_o @ A_75 @ B_38 ) ) ) ) )).

thf(fact_999_Int__insert__right,axiom,(
    ! [B_38: pname > $o,A_76: pname,A_75: pname > $o] :
      ( ( ( member_pname @ A_76 @ A_75 )
       => ( ( semila1673364395name_o @ A_75 @ ( insert_pname @ A_76 @ B_38 ) )
          = ( insert_pname @ A_76 @ ( semila1673364395name_o @ A_75 @ B_38 ) ) ) )
      & ( ~ ( member_pname @ A_76 @ A_75 )
       => ( ( semila1673364395name_o @ A_75 @ ( insert_pname @ A_76 @ B_38 ) )
          = ( semila1673364395name_o @ A_75 @ B_38 ) ) ) ) )).

thf(fact_1000_Int__insert__right,axiom,(
    ! [B_38: hoare_1708887482_state > $o,A_76: hoare_1708887482_state,A_75: hoare_1708887482_state > $o] :
      ( ( ( member451959335_state @ A_76 @ A_75 )
       => ( ( semila129691299tate_o @ A_75 @ ( insert528405184_state @ A_76 @ B_38 ) )
          = ( insert528405184_state @ A_76 @ ( semila129691299tate_o @ A_75 @ B_38 ) ) ) )
      & ( ~ ( member451959335_state @ A_76 @ A_75 )
       => ( ( semila129691299tate_o @ A_75 @ ( insert528405184_state @ A_76 @ B_38 ) )
          = ( semila129691299tate_o @ A_75 @ B_38 ) ) ) ) )).

thf(fact_1001_Int__mono,axiom,(
    ! [B_37: pname > $o,D: pname > $o,A_74: pname > $o,C_12: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_74 @ C_12 )
     => ( ( ord_less_eq_pname_o @ B_37 @ D )
       => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_74 @ B_37 ) @ ( semila1673364395name_o @ C_12 @ D ) ) ) ) )).

thf(fact_1002_Int__mono,axiom,(
    ! [B_37: hoare_1708887482_state > $o,D: hoare_1708887482_state > $o,A_74: hoare_1708887482_state > $o,C_12: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_74 @ C_12 )
     => ( ( ord_le777019615tate_o @ B_37 @ D )
       => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_74 @ B_37 ) @ ( semila129691299tate_o @ C_12 @ D ) ) ) ) )).

thf(fact_1003_Int__greatest,axiom,(
    ! [B_36: pname > $o,C_11: pname > $o,A_73: pname > $o] :
      ( ( ord_less_eq_pname_o @ C_11 @ A_73 )
     => ( ( ord_less_eq_pname_o @ C_11 @ B_36 )
       => ( ord_less_eq_pname_o @ C_11 @ ( semila1673364395name_o @ A_73 @ B_36 ) ) ) ) )).

thf(fact_1004_Int__greatest,axiom,(
    ! [B_36: hoare_1708887482_state > $o,C_11: hoare_1708887482_state > $o,A_73: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ C_11 @ A_73 )
     => ( ( ord_le777019615tate_o @ C_11 @ B_36 )
       => ( ord_le777019615tate_o @ C_11 @ ( semila129691299tate_o @ A_73 @ B_36 ) ) ) ) )).

thf(fact_1005_Int__absorb1,axiom,(
    ! [B_35: pname > $o,A_72: pname > $o] :
      ( ( ord_less_eq_pname_o @ B_35 @ A_72 )
     => ( ( semila1673364395name_o @ A_72 @ B_35 )
        = B_35 ) ) )).

thf(fact_1006_Int__absorb1,axiom,(
    ! [B_35: hoare_1708887482_state > $o,A_72: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ B_35 @ A_72 )
     => ( ( semila129691299tate_o @ A_72 @ B_35 )
        = B_35 ) ) )).

thf(fact_1007_Int__absorb2,axiom,(
    ! [A_71: pname > $o,B_34: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_71 @ B_34 )
     => ( ( semila1673364395name_o @ A_71 @ B_34 )
        = A_71 ) ) )).

thf(fact_1008_Int__absorb2,axiom,(
    ! [A_71: hoare_1708887482_state > $o,B_34: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_71 @ B_34 )
     => ( ( semila129691299tate_o @ A_71 @ B_34 )
        = A_71 ) ) )).

thf(fact_1009_Int__lower2,axiom,(
    ! [A_70: pname > $o,B_33: pname > $o] :
      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_70 @ B_33 ) @ B_33 ) )).

thf(fact_1010_Int__lower2,axiom,(
    ! [A_70: hoare_1708887482_state > $o,B_33: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_70 @ B_33 ) @ B_33 ) )).

thf(fact_1011_Int__lower1,axiom,(
    ! [A_69: pname > $o,B_32: pname > $o] :
      ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_69 @ B_32 ) @ A_69 ) )).

thf(fact_1012_Int__lower1,axiom,(
    ! [A_69: hoare_1708887482_state > $o,B_32: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_69 @ B_32 ) @ A_69 ) )).

thf(fact_1013_Un__Int__crazy,axiom,(
    ! [A_68: pname > $o,B_31: pname > $o,C_10: pname > $o] :
      ( ( semila1780557381name_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ A_68 @ B_31 ) @ ( semila1673364395name_o @ B_31 @ C_10 ) ) @ ( semila1673364395name_o @ C_10 @ A_68 ) )
      = ( semila1673364395name_o @ ( semila1673364395name_o @ ( semila1780557381name_o @ A_68 @ B_31 ) @ ( semila1780557381name_o @ B_31 @ C_10 ) ) @ ( semila1780557381name_o @ C_10 @ A_68 ) ) ) )).

thf(fact_1014_Un__Int__crazy,axiom,(
    ! [A_68: hoare_1708887482_state > $o,B_31: hoare_1708887482_state > $o,C_10: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ ( semila1122118281tate_o @ ( semila129691299tate_o @ A_68 @ B_31 ) @ ( semila129691299tate_o @ B_31 @ C_10 ) ) @ ( semila129691299tate_o @ C_10 @ A_68 ) )
      = ( semila129691299tate_o @ ( semila129691299tate_o @ ( semila1122118281tate_o @ A_68 @ B_31 ) @ ( semila1122118281tate_o @ B_31 @ C_10 ) ) @ ( semila1122118281tate_o @ C_10 @ A_68 ) ) ) )).

thf(fact_1015_Un__Int__distrib2,axiom,(
    ! [B_30: pname > $o,C_9: pname > $o,A_67: pname > $o] :
      ( ( semila1780557381name_o @ ( semila1673364395name_o @ B_30 @ C_9 ) @ A_67 )
      = ( semila1673364395name_o @ ( semila1780557381name_o @ B_30 @ A_67 ) @ ( semila1780557381name_o @ C_9 @ A_67 ) ) ) )).

thf(fact_1016_Un__Int__distrib2,axiom,(
    ! [B_30: hoare_1708887482_state > $o,C_9: hoare_1708887482_state > $o,A_67: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ ( semila129691299tate_o @ B_30 @ C_9 ) @ A_67 )
      = ( semila129691299tate_o @ ( semila1122118281tate_o @ B_30 @ A_67 ) @ ( semila1122118281tate_o @ C_9 @ A_67 ) ) ) )).

thf(fact_1017_Int__Un__distrib2,axiom,(
    ! [B_29: pname > $o,C_8: pname > $o,A_66: pname > $o] :
      ( ( semila1673364395name_o @ ( semila1780557381name_o @ B_29 @ C_8 ) @ A_66 )
      = ( semila1780557381name_o @ ( semila1673364395name_o @ B_29 @ A_66 ) @ ( semila1673364395name_o @ C_8 @ A_66 ) ) ) )).

thf(fact_1018_Int__Un__distrib2,axiom,(
    ! [B_29: hoare_1708887482_state > $o,C_8: hoare_1708887482_state > $o,A_66: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ ( semila1122118281tate_o @ B_29 @ C_8 ) @ A_66 )
      = ( semila1122118281tate_o @ ( semila129691299tate_o @ B_29 @ A_66 ) @ ( semila129691299tate_o @ C_8 @ A_66 ) ) ) )).

thf(fact_1019_Un__Int__distrib,axiom,(
    ! [A_65: pname > $o,B_28: pname > $o,C_7: pname > $o] :
      ( ( semila1780557381name_o @ A_65 @ ( semila1673364395name_o @ B_28 @ C_7 ) )
      = ( semila1673364395name_o @ ( semila1780557381name_o @ A_65 @ B_28 ) @ ( semila1780557381name_o @ A_65 @ C_7 ) ) ) )).

thf(fact_1020_Un__Int__distrib,axiom,(
    ! [A_65: hoare_1708887482_state > $o,B_28: hoare_1708887482_state > $o,C_7: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ A_65 @ ( semila129691299tate_o @ B_28 @ C_7 ) )
      = ( semila129691299tate_o @ ( semila1122118281tate_o @ A_65 @ B_28 ) @ ( semila1122118281tate_o @ A_65 @ C_7 ) ) ) )).

thf(fact_1021_Int__Un__distrib,axiom,(
    ! [A_64: pname > $o,B_27: pname > $o,C_6: pname > $o] :
      ( ( semila1673364395name_o @ A_64 @ ( semila1780557381name_o @ B_27 @ C_6 ) )
      = ( semila1780557381name_o @ ( semila1673364395name_o @ A_64 @ B_27 ) @ ( semila1673364395name_o @ A_64 @ C_6 ) ) ) )).

thf(fact_1022_Int__Un__distrib,axiom,(
    ! [A_64: hoare_1708887482_state > $o,B_27: hoare_1708887482_state > $o,C_6: hoare_1708887482_state > $o] :
      ( ( semila129691299tate_o @ A_64 @ ( semila1122118281tate_o @ B_27 @ C_6 ) )
      = ( semila1122118281tate_o @ ( semila129691299tate_o @ A_64 @ B_27 ) @ ( semila129691299tate_o @ A_64 @ C_6 ) ) ) )).

thf(fact_1023_distrib__inf__le,axiom,(
    ! [X_20: $o,Y_9: $o,Z_4: $o] :
      ( ord_less_eq_o @ ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_20 @ Y_9 ) @ ( semila854092349_inf_o @ X_20 @ Z_4 ) ) @ ( semila854092349_inf_o @ X_20 @ ( semila10642723_sup_o @ Y_9 @ Z_4 ) ) ) )).

thf(fact_1024_distrib__inf__le,axiom,(
    ! [X_20: pname > $o,Y_9: pname > $o,Z_4: pname > $o] :
      ( ord_less_eq_pname_o @ ( semila1780557381name_o @ ( semila1673364395name_o @ X_20 @ Y_9 ) @ ( semila1673364395name_o @ X_20 @ Z_4 ) ) @ ( semila1673364395name_o @ X_20 @ ( semila1780557381name_o @ Y_9 @ Z_4 ) ) ) )).

thf(fact_1025_distrib__inf__le,axiom,(
    ! [X_20: hoare_1708887482_state > $o,Y_9: hoare_1708887482_state > $o,Z_4: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ ( semila1122118281tate_o @ ( semila129691299tate_o @ X_20 @ Y_9 ) @ ( semila129691299tate_o @ X_20 @ Z_4 ) ) @ ( semila129691299tate_o @ X_20 @ ( semila1122118281tate_o @ Y_9 @ Z_4 ) ) ) )).

thf(fact_1026_distrib__sup__le,axiom,(
    ! [X_19: $o,Y_8: $o,Z_3: $o] :
      ( ord_less_eq_o @ ( semila10642723_sup_o @ X_19 @ ( semila854092349_inf_o @ Y_8 @ Z_3 ) ) @ ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_19 @ Y_8 ) @ ( semila10642723_sup_o @ X_19 @ Z_3 ) ) ) )).

thf(fact_1027_distrib__sup__le,axiom,(
    ! [X_19: pname > $o,Y_8: pname > $o,Z_3: pname > $o] :
      ( ord_less_eq_pname_o @ ( semila1780557381name_o @ X_19 @ ( semila1673364395name_o @ Y_8 @ Z_3 ) ) @ ( semila1673364395name_o @ ( semila1780557381name_o @ X_19 @ Y_8 ) @ ( semila1780557381name_o @ X_19 @ Z_3 ) ) ) )).

thf(fact_1028_distrib__sup__le,axiom,(
    ! [X_19: hoare_1708887482_state > $o,Y_8: hoare_1708887482_state > $o,Z_3: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ ( semila1122118281tate_o @ X_19 @ ( semila129691299tate_o @ Y_8 @ Z_3 ) ) @ ( semila129691299tate_o @ ( semila1122118281tate_o @ X_19 @ Y_8 ) @ ( semila1122118281tate_o @ X_19 @ Z_3 ) ) ) )).

thf(fact_1029_insert__Diff,axiom,(
    ! [A_63: com,A_62: com > $o] :
      ( ( member_com @ A_63 @ A_62 )
     => ( ( insert_com @ A_63 @ ( minus_minus_com_o @ A_62 @ ( insert_com @ A_63 @ bot_bot_com_o ) ) )
        = A_62 ) ) )).

thf(fact_1030_insert__Diff,axiom,(
    ! [A_63: pname,A_62: pname > $o] :
      ( ( member_pname @ A_63 @ A_62 )
     => ( ( insert_pname @ A_63 @ ( minus_minus_pname_o @ A_62 @ ( insert_pname @ A_63 @ bot_bot_pname_o ) ) )
        = A_62 ) ) )).

thf(fact_1031_insert__Diff,axiom,(
    ! [A_63: hoare_1708887482_state,A_62: hoare_1708887482_state > $o] :
      ( ( member451959335_state @ A_63 @ A_62 )
     => ( ( insert528405184_state @ A_63 @ ( minus_2056855718tate_o @ A_62 @ ( insert528405184_state @ A_63 @ bot_bo19817387tate_o ) ) )
        = A_62 ) ) )).

thf(fact_1032_Diff__insert__absorb,axiom,(
    ! [X_18: com,A_61: com > $o] :
      ( ~ ( member_com @ X_18 @ A_61 )
     => ( ( minus_minus_com_o @ ( insert_com @ X_18 @ A_61 ) @ ( insert_com @ X_18 @ bot_bot_com_o ) )
        = A_61 ) ) )).

thf(fact_1033_Diff__insert__absorb,axiom,(
    ! [X_18: pname,A_61: pname > $o] :
      ( ~ ( member_pname @ X_18 @ A_61 )
     => ( ( minus_minus_pname_o @ ( insert_pname @ X_18 @ A_61 ) @ ( insert_pname @ X_18 @ bot_bot_pname_o ) )
        = A_61 ) ) )).

thf(fact_1034_Diff__insert__absorb,axiom,(
    ! [X_18: hoare_1708887482_state,A_61: hoare_1708887482_state > $o] :
      ( ~ ( member451959335_state @ X_18 @ A_61 )
     => ( ( minus_2056855718tate_o @ ( insert528405184_state @ X_18 @ A_61 ) @ ( insert528405184_state @ X_18 @ bot_bo19817387tate_o ) )
        = A_61 ) ) )).

thf(fact_1035_insert__Diff__single,axiom,(
    ! [A_60: com,A_59: com > $o] :
      ( ( insert_com @ A_60 @ ( minus_minus_com_o @ A_59 @ ( insert_com @ A_60 @ bot_bot_com_o ) ) )
      = ( insert_com @ A_60 @ A_59 ) ) )).

thf(fact_1036_insert__Diff__single,axiom,(
    ! [A_60: pname,A_59: pname > $o] :
      ( ( insert_pname @ A_60 @ ( minus_minus_pname_o @ A_59 @ ( insert_pname @ A_60 @ bot_bot_pname_o ) ) )
      = ( insert_pname @ A_60 @ A_59 ) ) )).

thf(fact_1037_insert__Diff__single,axiom,(
    ! [A_60: hoare_1708887482_state,A_59: hoare_1708887482_state > $o] :
      ( ( insert528405184_state @ A_60 @ ( minus_2056855718tate_o @ A_59 @ ( insert528405184_state @ A_60 @ bot_bo19817387tate_o ) ) )
      = ( insert528405184_state @ A_60 @ A_59 ) ) )).

thf(fact_1038_Diff__insert2,axiom,(
    ! [A_58: com > $o,A_57: com,B_26: com > $o] :
      ( ( minus_minus_com_o @ A_58 @ ( insert_com @ A_57 @ B_26 ) )
      = ( minus_minus_com_o @ ( minus_minus_com_o @ A_58 @ ( insert_com @ A_57 @ bot_bot_com_o ) ) @ B_26 ) ) )).

thf(fact_1039_Diff__insert2,axiom,(
    ! [A_58: pname > $o,A_57: pname,B_26: pname > $o] :
      ( ( minus_minus_pname_o @ A_58 @ ( insert_pname @ A_57 @ B_26 ) )
      = ( minus_minus_pname_o @ ( minus_minus_pname_o @ A_58 @ ( insert_pname @ A_57 @ bot_bot_pname_o ) ) @ B_26 ) ) )).

thf(fact_1040_Diff__insert2,axiom,(
    ! [A_58: hoare_1708887482_state > $o,A_57: hoare_1708887482_state,B_26: hoare_1708887482_state > $o] :
      ( ( minus_2056855718tate_o @ A_58 @ ( insert528405184_state @ A_57 @ B_26 ) )
      = ( minus_2056855718tate_o @ ( minus_2056855718tate_o @ A_58 @ ( insert528405184_state @ A_57 @ bot_bo19817387tate_o ) ) @ B_26 ) ) )).

thf(fact_1041_Diff__insert,axiom,(
    ! [A_56: com > $o,A_55: com,B_25: com > $o] :
      ( ( minus_minus_com_o @ A_56 @ ( insert_com @ A_55 @ B_25 ) )
      = ( minus_minus_com_o @ ( minus_minus_com_o @ A_56 @ B_25 ) @ ( insert_com @ A_55 @ bot_bot_com_o ) ) ) )).

thf(fact_1042_Diff__insert,axiom,(
    ! [A_56: pname > $o,A_55: pname,B_25: pname > $o] :
      ( ( minus_minus_pname_o @ A_56 @ ( insert_pname @ A_55 @ B_25 ) )
      = ( minus_minus_pname_o @ ( minus_minus_pname_o @ A_56 @ B_25 ) @ ( insert_pname @ A_55 @ bot_bot_pname_o ) ) ) )).

thf(fact_1043_Diff__insert,axiom,(
    ! [A_56: hoare_1708887482_state > $o,A_55: hoare_1708887482_state,B_25: hoare_1708887482_state > $o] :
      ( ( minus_2056855718tate_o @ A_56 @ ( insert528405184_state @ A_55 @ B_25 ) )
      = ( minus_2056855718tate_o @ ( minus_2056855718tate_o @ A_56 @ B_25 ) @ ( insert528405184_state @ A_55 @ bot_bo19817387tate_o ) ) ) )).

thf(fact_1044_finite__Diff__insert,axiom,(
    ! [A_54: com > $o,A_53: com,B_24: com > $o] :
      ( ( finite_finite_com @ ( minus_minus_com_o @ A_54 @ ( insert_com @ A_53 @ B_24 ) ) )
    <=> ( finite_finite_com @ ( minus_minus_com_o @ A_54 @ B_24 ) ) ) )).

thf(fact_1045_finite__Diff__insert,axiom,(
    ! [A_54: pname > $o,A_53: pname,B_24: pname > $o] :
      ( ( finite_finite_pname @ ( minus_minus_pname_o @ A_54 @ ( insert_pname @ A_53 @ B_24 ) ) )
    <=> ( finite_finite_pname @ ( minus_minus_pname_o @ A_54 @ B_24 ) ) ) )).

thf(fact_1046_finite__Diff__insert,axiom,(
    ! [A_54: hoare_1708887482_state > $o,A_53: hoare_1708887482_state,B_24: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ ( minus_2056855718tate_o @ A_54 @ ( insert528405184_state @ A_53 @ B_24 ) ) )
    <=> ( finite1625599783_state @ ( minus_2056855718tate_o @ A_54 @ B_24 ) ) ) )).

thf(fact_1047_finite__Diff__insert,axiom,(
    ! [A_54: ( pname > $o ) > $o,A_53: pname > $o,B_24: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_54 @ ( insert_pname_o @ A_53 @ B_24 ) ) )
    <=> ( finite297249702name_o @ ( minus_1480864103me_o_o @ A_54 @ B_24 ) ) ) )).

thf(fact_1048_finite__Diff__insert,axiom,(
    ! [A_54: ( hoare_1708887482_state > $o ) > $o,A_53: hoare_1708887482_state > $o,B_24: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_54 @ ( insert949073679tate_o @ A_53 @ B_24 ) ) )
    <=> ( finite1329924456tate_o @ ( minus_548038231te_o_o @ A_54 @ B_24 ) ) ) )).

thf(fact_1049_image__diff__subset,axiom,(
    ! [F_27: pname > hoare_1708887482_state,A_52: pname > $o,B_23: pname > $o] :
      ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ ( image_1116629049_state @ F_27 @ A_52 ) @ ( image_1116629049_state @ F_27 @ B_23 ) ) @ ( image_1116629049_state @ F_27 @ ( minus_minus_pname_o @ A_52 @ B_23 ) ) ) )).

thf(fact_1050_Diff__partition,axiom,(
    ! [A_51: pname > $o,B_22: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_51 @ B_22 )
     => ( ( semila1780557381name_o @ A_51 @ ( minus_minus_pname_o @ B_22 @ A_51 ) )
        = B_22 ) ) )).

thf(fact_1051_Diff__partition,axiom,(
    ! [A_51: hoare_1708887482_state > $o,B_22: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_51 @ B_22 )
     => ( ( semila1122118281tate_o @ A_51 @ ( minus_2056855718tate_o @ B_22 @ A_51 ) )
        = B_22 ) ) )).

thf(fact_1052_Diff__subset__conv,axiom,(
    ! [A_50: pname > $o,B_21: pname > $o,C_5: pname > $o] :
      ( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_50 @ B_21 ) @ C_5 )
    <=> ( ord_less_eq_pname_o @ A_50 @ ( semila1780557381name_o @ B_21 @ C_5 ) ) ) )).

thf(fact_1053_Diff__subset__conv,axiom,(
    ! [A_50: hoare_1708887482_state > $o,B_21: hoare_1708887482_state > $o,C_5: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_50 @ B_21 ) @ C_5 )
    <=> ( ord_le777019615tate_o @ A_50 @ ( semila1122118281tate_o @ B_21 @ C_5 ) ) ) )).

thf(fact_1054_image__Int__subset,axiom,(
    ! [F_26: pname > hoare_1708887482_state,A_49: pname > $o,B_20: pname > $o] :
      ( ord_le777019615tate_o @ ( image_1116629049_state @ F_26 @ ( semila1673364395name_o @ A_49 @ B_20 ) ) @ ( semila129691299tate_o @ ( image_1116629049_state @ F_26 @ A_49 ) @ ( image_1116629049_state @ F_26 @ B_20 ) ) ) )).

thf(fact_1055_Un__Int__assoc__eq,axiom,(
    ! [A_48: pname > $o,B_19: pname > $o,C_4: pname > $o] :
      ( ( ( semila1780557381name_o @ ( semila1673364395name_o @ A_48 @ B_19 ) @ C_4 )
        = ( semila1673364395name_o @ A_48 @ ( semila1780557381name_o @ B_19 @ C_4 ) ) )
    <=> ( ord_less_eq_pname_o @ C_4 @ A_48 ) ) )).

thf(fact_1056_Un__Int__assoc__eq,axiom,(
    ! [A_48: hoare_1708887482_state > $o,B_19: hoare_1708887482_state > $o,C_4: hoare_1708887482_state > $o] :
      ( ( ( semila1122118281tate_o @ ( semila129691299tate_o @ A_48 @ B_19 ) @ C_4 )
        = ( semila129691299tate_o @ A_48 @ ( semila1122118281tate_o @ B_19 @ C_4 ) ) )
    <=> ( ord_le777019615tate_o @ C_4 @ A_48 ) ) )).

thf(fact_1057_if__image__distrib,axiom,(
    ! [P_4: pname > $o,F_25: pname > hoare_1708887482_state,G_4: pname > hoare_1708887482_state,S: pname > $o] :
      ( ( image_1116629049_state
        @ ^ [X_3: pname] :
            ( if_Hoa1374726218_state @ ( P_4 @ X_3 ) @ ( F_25 @ X_3 ) @ ( G_4 @ X_3 ) )
        @ S )
      = ( semila1122118281tate_o @ ( image_1116629049_state @ F_25 @ ( semila1673364395name_o @ S @ ( collect_pname @ P_4 ) ) )
        @ ( image_1116629049_state @ G_4
          @ ( semila1673364395name_o @ S
            @ ( collect_pname
              @ ^ [X_3: pname] :
                  ( (~) @ ( P_4 @ X_3 ) ) ) ) ) ) ) )).

thf(fact_1058_dom__if,axiom,(
    ! [P_3: pname > $o,F_24: pname > option_com,G_3: pname > option_com] :
      ( ( dom_pname_com
        @ ^ [X_3: pname] :
            ( if_option_com @ ( P_3 @ X_3 ) @ ( F_24 @ X_3 ) @ ( G_3 @ X_3 ) ) )
      = ( semila1780557381name_o @ ( semila1673364395name_o @ ( dom_pname_com @ F_24 ) @ ( collect_pname @ P_3 ) )
        @ ( semila1673364395name_o @ ( dom_pname_com @ G_3 )
          @ ( collect_pname
            @ ^ [X_3: pname] :
                ( (~) @ ( P_3 @ X_3 ) ) ) ) ) ) )).

thf(fact_1059_diff__single__insert,axiom,(
    ! [A_47: com > $o,X_17: com,B_18: com > $o] :
      ( ( ord_less_eq_com_o @ ( minus_minus_com_o @ A_47 @ ( insert_com @ X_17 @ bot_bot_com_o ) ) @ B_18 )
     => ( ( member_com @ X_17 @ A_47 )
       => ( ord_less_eq_com_o @ A_47 @ ( insert_com @ X_17 @ B_18 ) ) ) ) )).

thf(fact_1060_diff__single__insert,axiom,(
    ! [A_47: pname > $o,X_17: pname,B_18: pname > $o] :
      ( ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_47 @ ( insert_pname @ X_17 @ bot_bot_pname_o ) ) @ B_18 )
     => ( ( member_pname @ X_17 @ A_47 )
       => ( ord_less_eq_pname_o @ A_47 @ ( insert_pname @ X_17 @ B_18 ) ) ) ) )).

thf(fact_1061_diff__single__insert,axiom,(
    ! [A_47: hoare_1708887482_state > $o,X_17: hoare_1708887482_state,B_18: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_47 @ ( insert528405184_state @ X_17 @ bot_bo19817387tate_o ) ) @ B_18 )
     => ( ( member451959335_state @ X_17 @ A_47 )
       => ( ord_le777019615tate_o @ A_47 @ ( insert528405184_state @ X_17 @ B_18 ) ) ) ) )).

thf(fact_1062_subset__insert__iff,axiom,(
    ! [A_46: com > $o,X_16: com,B_17: com > $o] :
      ( ( ord_less_eq_com_o @ A_46 @ ( insert_com @ X_16 @ B_17 ) )
    <=> ( ( ( member_com @ X_16 @ A_46 )
         => ( ord_less_eq_com_o @ ( minus_minus_com_o @ A_46 @ ( insert_com @ X_16 @ bot_bot_com_o ) ) @ B_17 ) )
        & ( ~ ( member_com @ X_16 @ A_46 )
         => ( ord_less_eq_com_o @ A_46 @ B_17 ) ) ) ) )).

thf(fact_1063_subset__insert__iff,axiom,(
    ! [A_46: pname > $o,X_16: pname,B_17: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_46 @ ( insert_pname @ X_16 @ B_17 ) )
    <=> ( ( ( member_pname @ X_16 @ A_46 )
         => ( ord_less_eq_pname_o @ ( minus_minus_pname_o @ A_46 @ ( insert_pname @ X_16 @ bot_bot_pname_o ) ) @ B_17 ) )
        & ( ~ ( member_pname @ X_16 @ A_46 )
         => ( ord_less_eq_pname_o @ A_46 @ B_17 ) ) ) ) )).

thf(fact_1064_subset__insert__iff,axiom,(
    ! [A_46: hoare_1708887482_state > $o,X_16: hoare_1708887482_state,B_17: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_46 @ ( insert528405184_state @ X_16 @ B_17 ) )
    <=> ( ( ( member451959335_state @ X_16 @ A_46 )
         => ( ord_le777019615tate_o @ ( minus_2056855718tate_o @ A_46 @ ( insert528405184_state @ X_16 @ bot_bo19817387tate_o ) ) @ B_17 ) )
        & ( ~ ( member451959335_state @ X_16 @ A_46 )
         => ( ord_le777019615tate_o @ A_46 @ B_17 ) ) ) ) )).

thf(fact_1065_finite__empty__induct,axiom,(
    ! [P_2: ( com > $o ) > $o,A_45: com > $o] :
      ( ( finite_finite_com @ A_45 )
     => ( ( P_2 @ A_45 )
       => ( ! [A_6: com,A_39: com > $o] :
              ( ( finite_finite_com @ A_39 )
             => ( ( member_com @ A_6 @ A_39 )
               => ( ( P_2 @ A_39 )
                 => ( P_2 @ ( minus_minus_com_o @ A_39 @ ( insert_com @ A_6 @ bot_bot_com_o ) ) ) ) ) )
         => ( P_2 @ bot_bot_com_o ) ) ) ) )).

thf(fact_1066_finite__empty__induct,axiom,(
    ! [P_2: ( pname > $o ) > $o,A_45: pname > $o] :
      ( ( finite_finite_pname @ A_45 )
     => ( ( P_2 @ A_45 )
       => ( ! [A_6: pname,A_39: pname > $o] :
              ( ( finite_finite_pname @ A_39 )
             => ( ( member_pname @ A_6 @ A_39 )
               => ( ( P_2 @ A_39 )
                 => ( P_2 @ ( minus_minus_pname_o @ A_39 @ ( insert_pname @ A_6 @ bot_bot_pname_o ) ) ) ) ) )
         => ( P_2 @ bot_bot_pname_o ) ) ) ) )).

thf(fact_1067_finite__empty__induct,axiom,(
    ! [P_2: ( hoare_1708887482_state > $o ) > $o,A_45: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_45 )
     => ( ( P_2 @ A_45 )
       => ( ! [A_6: hoare_1708887482_state,A_39: hoare_1708887482_state > $o] :
              ( ( finite1625599783_state @ A_39 )
             => ( ( member451959335_state @ A_6 @ A_39 )
               => ( ( P_2 @ A_39 )
                 => ( P_2 @ ( minus_2056855718tate_o @ A_39 @ ( insert528405184_state @ A_6 @ bot_bo19817387tate_o ) ) ) ) ) )
         => ( P_2 @ bot_bo19817387tate_o ) ) ) ) )).

thf(fact_1068_finite__empty__induct,axiom,(
    ! [P_2: ( ( pname > $o ) > $o ) > $o,A_45: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_45 )
     => ( ( P_2 @ A_45 )
       => ( ! [A_6: pname > $o,A_39: ( pname > $o ) > $o] :
              ( ( finite297249702name_o @ A_39 )
             => ( ( member_pname_o @ A_6 @ A_39 )
               => ( ( P_2 @ A_39 )
                 => ( P_2 @ ( minus_1480864103me_o_o @ A_39 @ ( insert_pname_o @ A_6 @ bot_bot_pname_o_o ) ) ) ) ) )
         => ( P_2 @ bot_bot_pname_o_o ) ) ) ) )).

thf(fact_1069_finite__empty__induct,axiom,(
    ! [P_2: ( ( hoare_1708887482_state > $o ) > $o ) > $o,A_45: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_45 )
     => ( ( P_2 @ A_45 )
       => ( ! [A_6: hoare_1708887482_state > $o,A_39: ( hoare_1708887482_state > $o ) > $o] :
              ( ( finite1329924456tate_o @ A_39 )
             => ( ( member814030440tate_o @ A_6 @ A_39 )
               => ( ( P_2 @ A_39 )
                 => ( P_2 @ ( minus_548038231te_o_o @ A_39 @ ( insert949073679tate_o @ A_6 @ bot_bo1678742418te_o_o ) ) ) ) ) )
         => ( P_2 @ bot_bo1678742418te_o_o ) ) ) ) )).

thf(fact_1070_dom__override__on,axiom,(
    ! [F_23: pname > option_com,G_2: pname > option_com,A_44: pname > $o] :
      ( ( dom_pname_com @ ( overri1496249029on_com @ F_23 @ G_2 @ A_44 ) )
      = ( semila1780557381name_o
        @ ( minus_minus_pname_o @ ( dom_pname_com @ F_23 )
          @ ( collect_pname
            @ ^ [A_6: pname] :
                ( member_pname @ A_6 @ ( minus_minus_pname_o @ A_44 @ ( dom_pname_com @ G_2 ) ) ) ) )
        @ ( collect_pname
          @ ^ [A_6: pname] :
              ( member_pname @ A_6 @ ( semila1673364395name_o @ A_44 @ ( dom_pname_com @ G_2 ) ) ) ) ) ) )).

thf(fact_1071_Int__Collect__mono,axiom,(
    ! [Q: com > $o,P_1: com > $o,A_43: com > $o,B_16: com > $o] :
      ( ( ord_less_eq_com_o @ A_43 @ B_16 )
     => ( ! [X_3: com] :
            ( ( member_com @ X_3 @ A_43 )
           => ( ( P_1 @ X_3 )
             => ( Q @ X_3 ) ) )
       => ( ord_less_eq_com_o @ ( semila513601829_com_o @ A_43 @ ( collect_com @ P_1 ) ) @ ( semila513601829_com_o @ B_16 @ ( collect_com @ Q ) ) ) ) ) )).

thf(fact_1072_Int__Collect__mono,axiom,(
    ! [Q: pname > $o,P_1: pname > $o,A_43: pname > $o,B_16: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_43 @ B_16 )
     => ( ! [X_3: pname] :
            ( ( member_pname @ X_3 @ A_43 )
           => ( ( P_1 @ X_3 )
             => ( Q @ X_3 ) ) )
       => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ A_43 @ ( collect_pname @ P_1 ) ) @ ( semila1673364395name_o @ B_16 @ ( collect_pname @ Q ) ) ) ) ) )).

thf(fact_1073_Int__Collect__mono,axiom,(
    ! [Q: hoare_1708887482_state > $o,P_1: hoare_1708887482_state > $o,A_43: hoare_1708887482_state > $o,B_16: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_43 @ B_16 )
     => ( ! [X_3: hoare_1708887482_state] :
            ( ( member451959335_state @ X_3 @ A_43 )
           => ( ( P_1 @ X_3 )
             => ( Q @ X_3 ) ) )
       => ( ord_le777019615tate_o @ ( semila129691299tate_o @ A_43 @ ( collec1568722789_state @ P_1 ) ) @ ( semila129691299tate_o @ B_16 @ ( collec1568722789_state @ Q ) ) ) ) ) )).

thf(fact_1074_Int__Collect__mono,axiom,(
    ! [Q: ( pname > $o ) > $o,P_1: ( pname > $o ) > $o,A_43: ( pname > $o ) > $o,B_16: ( pname > $o ) > $o] :
      ( ( ord_le1205211808me_o_o @ A_43 @ B_16 )
     => ( ! [X_3: pname > $o] :
            ( ( member_pname_o @ X_3 @ A_43 )
           => ( ( P_1 @ X_3 )
             => ( Q @ X_3 ) ) )
       => ( ord_le1205211808me_o_o @ ( semila2013987940me_o_o @ A_43 @ ( collect_pname_o @ P_1 ) ) @ ( semila2013987940me_o_o @ B_16 @ ( collect_pname_o @ Q ) ) ) ) ) )).

thf(fact_1075_Int__Collect__mono,axiom,(
    ! [Q: ( hoare_1708887482_state > $o ) > $o,P_1: ( hoare_1708887482_state > $o ) > $o,A_43: ( hoare_1708887482_state > $o ) > $o,B_16: ( hoare_1708887482_state > $o ) > $o] :
      ( ( ord_le1728773982te_o_o @ A_43 @ B_16 )
     => ( ! [X_3: hoare_1708887482_state > $o] :
            ( ( member814030440tate_o @ X_3 @ A_43 )
           => ( ( P_1 @ X_3 )
             => ( Q @ X_3 ) ) )
       => ( ord_le1728773982te_o_o @ ( semila598060698te_o_o @ A_43 @ ( collec219771562tate_o @ P_1 ) ) @ ( semila598060698te_o_o @ B_16 @ ( collec219771562tate_o @ Q ) ) ) ) ) )).

thf(fact_1076_distrib__imp2,axiom,(
    ! [X_15: $o,Y_7: $o,Z_2: $o] :
      ( ! [X_3: $o,Y_4: $o,Z_1: $o] :
          ( ( semila10642723_sup_o @ X_3 @ ( semila854092349_inf_o @ Y_4 @ Z_1 ) )
        <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_3 @ Y_4 ) @ ( semila10642723_sup_o @ X_3 @ Z_1 ) ) )
     => ( ( semila854092349_inf_o @ X_15 @ ( semila10642723_sup_o @ Y_7 @ Z_2 ) )
      <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_15 @ Y_7 ) @ ( semila854092349_inf_o @ X_15 @ Z_2 ) ) ) ) )).

thf(fact_1077_distrib__imp2,axiom,(
    ! [X_15: pname > $o,Y_7: pname > $o,Z_2: pname > $o] :
      ( ! [X_3: pname > $o,Y_4: pname > $o,Z_1: pname > $o] :
          ( ( semila1780557381name_o @ X_3 @ ( semila1673364395name_o @ Y_4 @ Z_1 ) )
          = ( semila1673364395name_o @ ( semila1780557381name_o @ X_3 @ Y_4 ) @ ( semila1780557381name_o @ X_3 @ Z_1 ) ) )
     => ( ( semila1673364395name_o @ X_15 @ ( semila1780557381name_o @ Y_7 @ Z_2 ) )
        = ( semila1780557381name_o @ ( semila1673364395name_o @ X_15 @ Y_7 ) @ ( semila1673364395name_o @ X_15 @ Z_2 ) ) ) ) )).

thf(fact_1078_distrib__imp2,axiom,(
    ! [X_15: hoare_1708887482_state > $o,Y_7: hoare_1708887482_state > $o,Z_2: hoare_1708887482_state > $o] :
      ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o,Z_1: hoare_1708887482_state > $o] :
          ( ( semila1122118281tate_o @ X_3 @ ( semila129691299tate_o @ Y_4 @ Z_1 ) )
          = ( semila129691299tate_o @ ( semila1122118281tate_o @ X_3 @ Y_4 ) @ ( semila1122118281tate_o @ X_3 @ Z_1 ) ) )
     => ( ( semila129691299tate_o @ X_15 @ ( semila1122118281tate_o @ Y_7 @ Z_2 ) )
        = ( semila1122118281tate_o @ ( semila129691299tate_o @ X_15 @ Y_7 ) @ ( semila129691299tate_o @ X_15 @ Z_2 ) ) ) ) )).

thf(fact_1079_distrib__imp1,axiom,(
    ! [X_14: $o,Y_6: $o,Z: $o] :
      ( ! [X_3: $o,Y_4: $o,Z_1: $o] :
          ( ( semila854092349_inf_o @ X_3 @ ( semila10642723_sup_o @ Y_4 @ Z_1 ) )
        <=> ( semila10642723_sup_o @ ( semila854092349_inf_o @ X_3 @ Y_4 ) @ ( semila854092349_inf_o @ X_3 @ Z_1 ) ) )
     => ( ( semila10642723_sup_o @ X_14 @ ( semila854092349_inf_o @ Y_6 @ Z ) )
      <=> ( semila854092349_inf_o @ ( semila10642723_sup_o @ X_14 @ Y_6 ) @ ( semila10642723_sup_o @ X_14 @ Z ) ) ) ) )).

thf(fact_1080_distrib__imp1,axiom,(
    ! [X_14: pname > $o,Y_6: pname > $o,Z: pname > $o] :
      ( ! [X_3: pname > $o,Y_4: pname > $o,Z_1: pname > $o] :
          ( ( semila1673364395name_o @ X_3 @ ( semila1780557381name_o @ Y_4 @ Z_1 ) )
          = ( semila1780557381name_o @ ( semila1673364395name_o @ X_3 @ Y_4 ) @ ( semila1673364395name_o @ X_3 @ Z_1 ) ) )
     => ( ( semila1780557381name_o @ X_14 @ ( semila1673364395name_o @ Y_6 @ Z ) )
        = ( semila1673364395name_o @ ( semila1780557381name_o @ X_14 @ Y_6 ) @ ( semila1780557381name_o @ X_14 @ Z ) ) ) ) )).

thf(fact_1081_distrib__imp1,axiom,(
    ! [X_14: hoare_1708887482_state > $o,Y_6: hoare_1708887482_state > $o,Z: hoare_1708887482_state > $o] :
      ( ! [X_3: hoare_1708887482_state > $o,Y_4: hoare_1708887482_state > $o,Z_1: hoare_1708887482_state > $o] :
          ( ( semila129691299tate_o @ X_3 @ ( semila1122118281tate_o @ Y_4 @ Z_1 ) )
          = ( semila1122118281tate_o @ ( semila129691299tate_o @ X_3 @ Y_4 ) @ ( semila129691299tate_o @ X_3 @ Z_1 ) ) )
     => ( ( semila1122118281tate_o @ X_14 @ ( semila129691299tate_o @ Y_6 @ Z ) )
        = ( semila129691299tate_o @ ( semila1122118281tate_o @ X_14 @ Y_6 ) @ ( semila1122118281tate_o @ X_14 @ Z ) ) ) ) )).

thf(fact_1082_flat__lub__def,axiom,(
    ! [A_42: com > $o,B_15: com] :
      ( ( ( ord_less_eq_com_o @ A_42 @ ( insert_com @ B_15 @ bot_bot_com_o ) )
       => ( ( partial_flat_lub_com @ B_15 @ A_42 )
          = B_15 ) )
      & ( ~ ( ord_less_eq_com_o @ A_42 @ ( insert_com @ B_15 @ bot_bot_com_o ) )
       => ( ( partial_flat_lub_com @ B_15 @ A_42 )
          = ( the_com_1
            @ ^ [X_3: com] :
                ( member_com @ X_3 @ ( minus_minus_com_o @ A_42 @ ( insert_com @ B_15 @ bot_bot_com_o ) ) ) ) ) ) ) )).

thf(fact_1083_flat__lub__def,axiom,(
    ! [A_42: pname > $o,B_15: pname] :
      ( ( ( ord_less_eq_pname_o @ A_42 @ ( insert_pname @ B_15 @ bot_bot_pname_o ) )
       => ( ( partia752020666_pname @ B_15 @ A_42 )
          = B_15 ) )
      & ( ~ ( ord_less_eq_pname_o @ A_42 @ ( insert_pname @ B_15 @ bot_bot_pname_o ) )
       => ( ( partia752020666_pname @ B_15 @ A_42 )
          = ( the_pname
            @ ^ [X_3: pname] :
                ( member_pname @ X_3 @ ( minus_minus_pname_o @ A_42 @ ( insert_pname @ B_15 @ bot_bot_pname_o ) ) ) ) ) ) ) )).

thf(fact_1084_flat__lub__def,axiom,(
    ! [A_42: hoare_1708887482_state > $o,B_15: hoare_1708887482_state] :
      ( ( ( ord_le777019615tate_o @ A_42 @ ( insert528405184_state @ B_15 @ bot_bo19817387tate_o ) )
       => ( ( partia1256728516_state @ B_15 @ A_42 )
          = B_15 ) )
      & ( ~ ( ord_le777019615tate_o @ A_42 @ ( insert528405184_state @ B_15 @ bot_bo19817387tate_o ) )
       => ( ( partia1256728516_state @ B_15 @ A_42 )
          = ( the_Ho851197897_state
            @ ^ [X_3: hoare_1708887482_state] :
                ( member451959335_state @ X_3 @ ( minus_2056855718tate_o @ A_42 @ ( insert528405184_state @ B_15 @ bot_bo19817387tate_o ) ) ) ) ) ) ) )).

thf(fact_1085_comp__fun__idem__remove,axiom,
    ( finite567462577_com_o
    @ ^ [X_3: com,A_39: com > $o] :
        ( minus_minus_com_o @ A_39 @ ( insert_com @ X_3 @ bot_bot_com_o ) ) )).

thf(fact_1086_comp__fun__idem__remove,axiom,
    ( finite1123817265name_o
    @ ^ [X_3: pname,A_39: pname > $o] :
        ( minus_minus_pname_o @ A_39 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) ) )).

thf(fact_1087_comp__fun__idem__remove,axiom,
    ( finite662762081tate_o
    @ ^ [X_3: hoare_1708887482_state,A_39: hoare_1708887482_state > $o] :
        ( minus_2056855718tate_o @ A_39 @ ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) ) )).

thf(fact_1088_fun__upd__image,axiom,(
    ! [F_22: pname > hoare_1708887482_state,Y_5: hoare_1708887482_state,X_13: pname,A_41: pname > $o] :
      ( ( ( member_pname @ X_13 @ A_41 )
       => ( ( image_1116629049_state @ ( fun_up1986763201_state @ F_22 @ X_13 @ Y_5 ) @ A_41 )
          = ( insert528405184_state @ Y_5 @ ( image_1116629049_state @ F_22 @ ( minus_minus_pname_o @ A_41 @ ( insert_pname @ X_13 @ bot_bot_pname_o ) ) ) ) ) )
      & ( ~ ( member_pname @ X_13 @ A_41 )
       => ( ( image_1116629049_state @ ( fun_up1986763201_state @ F_22 @ X_13 @ Y_5 ) @ A_41 )
          = ( image_1116629049_state @ F_22 @ A_41 ) ) ) ) )).

thf(fact_1089_comp__fun__idem__insert,axiom,
    ( finite567462577_com_o @ insert_com )).

thf(fact_1090_comp__fun__idem__insert,axiom,
    ( finite1123817265name_o @ insert_pname )).

thf(fact_1091_comp__fun__idem__insert,axiom,
    ( finite662762081tate_o @ insert528405184_state )).

thf(fact_1092_comp__fun__idem__sup,axiom,
    ( finite2048025996em_o_o @ semila10642723_sup_o )).

thf(fact_1093_comp__fun__idem__sup,axiom,
    ( finite138924780name_o @ semila1780557381name_o )).

thf(fact_1094_comp__fun__idem__sup,axiom,
    ( finite2034616076tate_o @ semila1122118281tate_o )).

thf(fact_1095_inj__on__Un,axiom,(
    ! [F_21: pname > hoare_1708887482_state,A_40: pname > $o,B_14: pname > $o] :
      ( ( inj_on1553129421_state @ F_21 @ ( semila1780557381name_o @ A_40 @ B_14 ) )
    <=> ( ( inj_on1553129421_state @ F_21 @ A_40 )
        & ( inj_on1553129421_state @ F_21 @ B_14 )
        & ( ( semila129691299tate_o @ ( image_1116629049_state @ F_21 @ ( minus_minus_pname_o @ A_40 @ B_14 ) ) @ ( image_1116629049_state @ F_21 @ ( minus_minus_pname_o @ B_14 @ A_40 ) ) )
          = bot_bo19817387tate_o ) ) ) )).

thf(fact_1096_dom__eq__singleton__conv,axiom,(
    ! [F_20: pname > option_com,X_12: pname] :
      ( ( ( dom_pname_com @ F_20 )
        = ( insert_pname @ X_12 @ bot_bot_pname_o ) )
    <=> ? [V: com] :
          ( F_20
          = ( fun_up879233478on_com
            @ ^ [X_3: pname] : none_com
            @ X_12
            @ ( some_com @ V ) ) ) ) )).

thf(fact_1097_minus__fold__remove,axiom,(
    ! [B_13: com > $o,A_38: com > $o] :
      ( ( finite_finite_com @ A_38 )
     => ( ( minus_minus_com_o @ B_13 @ A_38 )
        = ( finite504235573_com_o
          @ ^ [X_3: com,A_39: com > $o] :
              ( minus_minus_com_o @ A_39 @ ( insert_com @ X_3 @ bot_bot_com_o ) )
          @ B_13
          @ A_38 ) ) ) )).

thf(fact_1098_minus__fold__remove,axiom,(
    ! [B_13: pname > $o,A_38: pname > $o] :
      ( ( finite_finite_pname @ A_38 )
     => ( ( minus_minus_pname_o @ B_13 @ A_38 )
        = ( finite603803317name_o
          @ ^ [X_3: pname,A_39: pname > $o] :
              ( minus_minus_pname_o @ A_39 @ ( insert_pname @ X_3 @ bot_bot_pname_o ) )
          @ B_13
          @ A_38 ) ) ) )).

thf(fact_1099_minus__fold__remove,axiom,(
    ! [B_13: hoare_1708887482_state > $o,A_38: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_38 )
     => ( ( minus_2056855718tate_o @ B_13 @ A_38 )
        = ( finite96880613tate_o
          @ ^ [X_3: hoare_1708887482_state,A_39: hoare_1708887482_state > $o] :
              ( minus_2056855718tate_o @ A_39 @ ( insert528405184_state @ X_3 @ bot_bo19817387tate_o ) )
          @ B_13
          @ A_38 ) ) ) )).

thf(fact_1100_minus__fold__remove,axiom,(
    ! [B_13: ( pname > $o ) > $o,A_38: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_38 )
     => ( ( minus_1480864103me_o_o @ B_13 @ A_38 )
        = ( finite1849951719me_o_o
          @ ^ [X_3: pname > $o,A_39: ( pname > $o ) > $o] :
              ( minus_1480864103me_o_o @ A_39 @ ( insert_pname_o @ X_3 @ bot_bot_pname_o_o ) )
          @ B_13
          @ A_38 ) ) ) )).

thf(fact_1101_minus__fold__remove,axiom,(
    ! [B_13: ( hoare_1708887482_state > $o ) > $o,A_38: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_38 )
     => ( ( minus_548038231te_o_o @ B_13 @ A_38 )
        = ( finite463603445te_o_o
          @ ^ [X_3: hoare_1708887482_state > $o,A_39: ( hoare_1708887482_state > $o ) > $o] :
              ( minus_548038231te_o_o @ A_39 @ ( insert949073679tate_o @ X_3 @ bot_bo1678742418te_o_o ) )
          @ B_13
          @ A_38 ) ) ) )).

thf(fact_1102_image__eq__fold__image,axiom,(
    ! [F_19: pname > hoare_1708887482_state,A_37: pname > $o] :
      ( ( finite_finite_pname @ A_37 )
     => ( ( image_1116629049_state @ F_19 @ A_37 )
        = ( finite2139561282_pname @ semila1122118281tate_o
          @ ^ [X_3: pname] :
              ( insert528405184_state @ ( F_19 @ X_3 ) @ bot_bo19817387tate_o )
          @ bot_bo19817387tate_o
          @ A_37 ) ) ) )).

thf(fact_1103_inj__Some,axiom,(
    ! [A_36: pname > $o] :
      ( inj_on737724108_pname @ some_pname @ A_36 ) )).

thf(fact_1104_inj__Some,axiom,(
    ! [A_36: hoare_1708887482_state > $o] :
      ( inj_on945311362_state @ some_H1974565227_state @ A_36 ) )).

thf(fact_1105_inj__Some,axiom,(
    ! [A_36: com > $o] :
      ( inj_on11367768on_com @ some_com @ A_36 ) )).

thf(fact_1106_option_Osimps_I2_J,axiom,(
    ! [A_35: com] :
      ( none_com
     != ( some_com @ A_35 ) ) )).

thf(fact_1107_option_Osimps_I2_J,axiom,(
    ! [A_35: pname] :
      ( none_pname
     != ( some_pname @ A_35 ) ) )).

thf(fact_1108_option_Osimps_I2_J,axiom,(
    ! [A_35: hoare_1708887482_state] :
      ( none_H1106584047_state
     != ( some_H1974565227_state @ A_35 ) ) )).

thf(fact_1109_option_Osimps_I3_J,axiom,(
    ! [A_34: com] :
      ( ( some_com @ A_34 )
     != none_com ) )).

thf(fact_1110_option_Osimps_I3_J,axiom,(
    ! [A_34: pname] :
      ( ( some_pname @ A_34 )
     != none_pname ) )).

thf(fact_1111_option_Osimps_I3_J,axiom,(
    ! [A_34: hoare_1708887482_state] :
      ( ( some_H1974565227_state @ A_34 )
     != none_H1106584047_state ) )).

thf(fact_1112_not__Some__eq,axiom,(
    ! [X_11: option_com] :
      ( ! [Y_4: com] :
          ( X_11
         != ( some_com @ Y_4 ) )
    <=> ( X_11 = none_com ) ) )).

thf(fact_1113_not__Some__eq,axiom,(
    ! [X_11: option_pname] :
      ( ! [Y_4: pname] :
          ( X_11
         != ( some_pname @ Y_4 ) )
    <=> ( X_11 = none_pname ) ) )).

thf(fact_1114_not__Some__eq,axiom,(
    ! [X_11: option1624383643_state] :
      ( ! [Y_4: hoare_1708887482_state] :
          ( X_11
         != ( some_H1974565227_state @ Y_4 ) )
    <=> ( X_11 = none_H1106584047_state ) ) )).

thf(fact_1115_not__None__eq,axiom,(
    ! [X_10: option_com] :
      ( ( X_10 != none_com )
    <=> ? [Y_4: com] :
          ( X_10
          = ( some_com @ Y_4 ) ) ) )).

thf(fact_1116_not__None__eq,axiom,(
    ! [X_10: option_pname] :
      ( ( X_10 != none_pname )
    <=> ? [Y_4: pname] :
          ( X_10
          = ( some_pname @ Y_4 ) ) ) )).

thf(fact_1117_not__None__eq,axiom,(
    ! [X_10: option1624383643_state] :
      ( ( X_10 != none_H1106584047_state )
    <=> ? [Y_4: hoare_1708887482_state] :
          ( X_10
          = ( some_H1974565227_state @ Y_4 ) ) ) )).

thf(fact_1118_dom__def,axiom,(
    ! [M_2: pname > option_com] :
      ( ( dom_pname_com @ M_2 )
      = ( collect_pname
        @ ^ [A_6: pname] :
            ( (~)
            @ ( ( M_2 @ A_6 )
              = none_com ) ) ) ) )).

thf(fact_1119_domIff,axiom,(
    ! [A_33: pname,M_1: pname > option_com] :
      ( ( member_pname @ A_33 @ ( dom_pname_com @ M_1 ) )
    <=> ( ( M_1 @ A_33 )
       != none_com ) ) )).

thf(fact_1120_finite__imageD,axiom,(
    ! [F_18: pname > hoare_1708887482_state,A_32: pname > $o] :
      ( ( finite1625599783_state @ ( image_1116629049_state @ F_18 @ A_32 ) )
     => ( ( inj_on1553129421_state @ F_18 @ A_32 )
       => ( finite_finite_pname @ A_32 ) ) ) )).

thf(fact_1121_inj__on__Un__image__eq__iff,axiom,(
    ! [F_17: pname > hoare_1708887482_state,A_31: pname > $o,B_12: pname > $o] :
      ( ( inj_on1553129421_state @ F_17 @ ( semila1780557381name_o @ A_31 @ B_12 ) )
     => ( ( ( image_1116629049_state @ F_17 @ A_31 )
          = ( image_1116629049_state @ F_17 @ B_12 ) )
      <=> ( A_31 = B_12 ) ) ) )).

thf(fact_1122_is__none__def,axiom,(
    ! [X_9: option_com] :
      ( ( is_none_com @ X_9 )
    <=> ( X_9 = none_com ) ) )).

thf(fact_1123_is__none__code_I1_J,axiom,
    ( is_none_com @ none_com )).

thf(fact_1124_inj__on__fun__updI,axiom,(
    ! [X_8: pname,Y_3: hoare_1708887482_state,F_16: pname > hoare_1708887482_state,A_30: pname > $o] :
      ( ( inj_on1553129421_state @ F_16 @ A_30 )
     => ( ~ ( member451959335_state @ Y_3 @ ( image_1116629049_state @ F_16 @ A_30 ) )
       => ( inj_on1553129421_state @ ( fun_up1986763201_state @ F_16 @ X_8 @ Y_3 ) @ A_30 ) ) ) )).

thf(fact_1125_sup__le__fold__sup,axiom,(
    ! [B_11: pname > $o,A_29: pname > $o,A_28: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_28 )
     => ( ( member_pname_o @ A_29 @ A_28 )
       => ( ord_less_eq_pname_o @ ( semila1780557381name_o @ A_29 @ B_11 ) @ ( finite472615016name_o @ semila1780557381name_o @ B_11 @ A_28 ) ) ) ) )).

thf(fact_1126_sup__le__fold__sup,axiom,(
    ! [B_11: hoare_1708887482_state > $o,A_29: hoare_1708887482_state > $o,A_28: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_28 )
     => ( ( member814030440tate_o @ A_29 @ A_28 )
       => ( ord_le777019615tate_o @ ( semila1122118281tate_o @ A_29 @ B_11 ) @ ( finite822533768tate_o @ semila1122118281tate_o @ B_11 @ A_28 ) ) ) ) )).

thf(fact_1127_sup__le__fold__sup,axiom,(
    ! [B_11: $o,A_29: $o,A_28: $o > $o] :
      ( ( finite_finite_o @ A_28 )
     => ( ( member_o @ A_29 @ A_28 )
       => ( ord_less_eq_o @ ( semila10642723_sup_o @ A_29 @ B_11 ) @ ( finite_fold_o_o @ semila10642723_sup_o @ B_11 @ A_28 ) ) ) ) )).

thf(fact_1128_fold__inf__le__inf,axiom,(
    ! [B_10: pname > $o,A_27: pname > $o,A_26: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_26 )
     => ( ( member_pname_o @ A_27 @ A_26 )
       => ( ord_less_eq_pname_o @ ( finite472615016name_o @ semila1673364395name_o @ B_10 @ A_26 ) @ ( semila1673364395name_o @ A_27 @ B_10 ) ) ) ) )).

thf(fact_1129_fold__inf__le__inf,axiom,(
    ! [B_10: hoare_1708887482_state > $o,A_27: hoare_1708887482_state > $o,A_26: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_26 )
     => ( ( member814030440tate_o @ A_27 @ A_26 )
       => ( ord_le777019615tate_o @ ( finite822533768tate_o @ semila129691299tate_o @ B_10 @ A_26 ) @ ( semila129691299tate_o @ A_27 @ B_10 ) ) ) ) )).

thf(fact_1130_fold__inf__le__inf,axiom,(
    ! [B_10: $o,A_27: $o,A_26: $o > $o] :
      ( ( finite_finite_o @ A_26 )
     => ( ( member_o @ A_27 @ A_26 )
       => ( ord_less_eq_o @ ( finite_fold_o_o @ semila854092349_inf_o @ B_10 @ A_26 ) @ ( semila854092349_inf_o @ A_27 @ B_10 ) ) ) ) )).

thf(fact_1131_fold__sup__insert,axiom,(
    ! [B_9: pname > $o,A_25: pname > $o,A_24: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_24 )
     => ( ( finite472615016name_o @ semila1780557381name_o @ B_9 @ ( insert_pname_o @ A_25 @ A_24 ) )
        = ( semila1780557381name_o @ A_25 @ ( finite472615016name_o @ semila1780557381name_o @ B_9 @ A_24 ) ) ) ) )).

thf(fact_1132_fold__sup__insert,axiom,(
    ! [B_9: hoare_1708887482_state > $o,A_25: hoare_1708887482_state > $o,A_24: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_24 )
     => ( ( finite822533768tate_o @ semila1122118281tate_o @ B_9 @ ( insert949073679tate_o @ A_25 @ A_24 ) )
        = ( semila1122118281tate_o @ A_25 @ ( finite822533768tate_o @ semila1122118281tate_o @ B_9 @ A_24 ) ) ) ) )).

thf(fact_1133_fold__sup__insert,axiom,(
    ! [B_9: $o,A_25: $o,A_24: $o > $o] :
      ( ( finite_finite_o @ A_24 )
     => ( ( finite_fold_o_o @ semila10642723_sup_o @ B_9 @ ( insert_o @ A_25 @ A_24 ) )
      <=> ( semila10642723_sup_o @ A_25 @ ( finite_fold_o_o @ semila10642723_sup_o @ B_9 @ A_24 ) ) ) ) )).

thf(fact_1134_fold__inf__insert,axiom,(
    ! [B_8: pname > $o,A_23: pname > $o,A_22: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_22 )
     => ( ( finite472615016name_o @ semila1673364395name_o @ B_8 @ ( insert_pname_o @ A_23 @ A_22 ) )
        = ( semila1673364395name_o @ A_23 @ ( finite472615016name_o @ semila1673364395name_o @ B_8 @ A_22 ) ) ) ) )).

thf(fact_1135_fold__inf__insert,axiom,(
    ! [B_8: hoare_1708887482_state > $o,A_23: hoare_1708887482_state > $o,A_22: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_22 )
     => ( ( finite822533768tate_o @ semila129691299tate_o @ B_8 @ ( insert949073679tate_o @ A_23 @ A_22 ) )
        = ( semila129691299tate_o @ A_23 @ ( finite822533768tate_o @ semila129691299tate_o @ B_8 @ A_22 ) ) ) ) )).

thf(fact_1136_dom__eq__empty__conv,axiom,(
    ! [F_15: pname > option_com] :
      ( ( ( dom_pname_com @ F_15 )
        = bot_bot_pname_o )
    <=> ! [X_3: pname] :
          ( ( F_15 @ X_3 )
          = none_com ) ) )).

thf(fact_1137_dom__empty,axiom,
    ( ( dom_pname_com
      @ ^ [X_3: pname] : none_com )
    = bot_bot_pname_o )).

thf(fact_1138_Option_Oset_Osimps_I1_J,axiom,
    ( ( set_com @ none_com )
    = bot_bot_com_o )).

thf(fact_1139_Option_Oset_Osimps_I1_J,axiom,
    ( ( set_pname @ none_pname )
    = bot_bot_pname_o )).

thf(fact_1140_Option_Oset_Osimps_I1_J,axiom,
    ( ( set_Ho525251890_state @ none_H1106584047_state )
    = bot_bo19817387tate_o )).

thf(fact_1141_set__empty__eq,axiom,(
    ! [Xo: option_com] :
      ( ( ( set_com @ Xo )
        = bot_bot_com_o )
    <=> ( Xo = none_com ) ) )).

thf(fact_1142_set__empty__eq,axiom,(
    ! [Xo: option_pname] :
      ( ( ( set_pname @ Xo )
        = bot_bot_pname_o )
    <=> ( Xo = none_pname ) ) )).

thf(fact_1143_set__empty__eq,axiom,(
    ! [Xo: option1624383643_state] :
      ( ( ( set_Ho525251890_state @ Xo )
        = bot_bo19817387tate_o )
    <=> ( Xo = none_H1106584047_state ) ) )).

thf(fact_1144_endo__inj__surj,axiom,(
    ! [F_14: ( pname > $o ) > pname > $o,A_21: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_21 )
     => ( ( ord_le1205211808me_o_o @ ( image_1085733413name_o @ F_14 @ A_21 ) @ A_21 )
       => ( ( inj_on691924881name_o @ F_14 @ A_21 )
         => ( ( image_1085733413name_o @ F_14 @ A_21 )
            = A_21 ) ) ) ) )).

thf(fact_1145_endo__inj__surj,axiom,(
    ! [F_14: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,A_21: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_21 )
     => ( ( ord_le1728773982te_o_o @ ( image_909543877tate_o @ F_14 @ A_21 ) @ A_21 )
       => ( ( inj_on176908593tate_o @ F_14 @ A_21 )
         => ( ( image_909543877tate_o @ F_14 @ A_21 )
            = A_21 ) ) ) ) )).

thf(fact_1146_endo__inj__surj,axiom,(
    ! [F_14: pname > pname,A_21: pname > $o] :
      ( ( finite_finite_pname @ A_21 )
     => ( ( ord_less_eq_pname_o @ ( image_pname_pname @ F_14 @ A_21 ) @ A_21 )
       => ( ( inj_on_pname_pname @ F_14 @ A_21 )
         => ( ( image_pname_pname @ F_14 @ A_21 )
            = A_21 ) ) ) ) )).

thf(fact_1147_endo__inj__surj,axiom,(
    ! [F_14: hoare_1708887482_state > hoare_1708887482_state,A_21: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_21 )
     => ( ( ord_le777019615tate_o @ ( image_757158439_state @ F_14 @ A_21 ) @ A_21 )
       => ( ( inj_on632008595_state @ F_14 @ A_21 )
         => ( ( image_757158439_state @ F_14 @ A_21 )
            = A_21 ) ) ) ) )).

thf(fact_1148_finite__surj__inj,axiom,(
    ! [F_13: ( pname > $o ) > pname > $o,A_20: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_20 )
     => ( ( ord_le1205211808me_o_o @ A_20 @ ( image_1085733413name_o @ F_13 @ A_20 ) )
       => ( inj_on691924881name_o @ F_13 @ A_20 ) ) ) )).

thf(fact_1149_finite__surj__inj,axiom,(
    ! [F_13: ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,A_20: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_20 )
     => ( ( ord_le1728773982te_o_o @ A_20 @ ( image_909543877tate_o @ F_13 @ A_20 ) )
       => ( inj_on176908593tate_o @ F_13 @ A_20 ) ) ) )).

thf(fact_1150_finite__surj__inj,axiom,(
    ! [F_13: pname > pname,A_20: pname > $o] :
      ( ( finite_finite_pname @ A_20 )
     => ( ( ord_less_eq_pname_o @ A_20 @ ( image_pname_pname @ F_13 @ A_20 ) )
       => ( inj_on_pname_pname @ F_13 @ A_20 ) ) ) )).

thf(fact_1151_finite__surj__inj,axiom,(
    ! [F_13: hoare_1708887482_state > hoare_1708887482_state,A_20: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_20 )
     => ( ( ord_le777019615tate_o @ A_20 @ ( image_757158439_state @ F_13 @ A_20 ) )
       => ( inj_on632008595_state @ F_13 @ A_20 ) ) ) )).

thf(fact_1152_inj__on__image__Int,axiom,(
    ! [B_7: pname > $o,A_19: pname > $o,F_12: pname > hoare_1708887482_state,C_3: pname > $o] :
      ( ( inj_on1553129421_state @ F_12 @ C_3 )
     => ( ( ord_less_eq_pname_o @ A_19 @ C_3 )
       => ( ( ord_less_eq_pname_o @ B_7 @ C_3 )
         => ( ( image_1116629049_state @ F_12 @ ( semila1673364395name_o @ A_19 @ B_7 ) )
            = ( semila129691299tate_o @ ( image_1116629049_state @ F_12 @ A_19 ) @ ( image_1116629049_state @ F_12 @ B_7 ) ) ) ) ) ) )).

thf(fact_1153_inj__on__image__set__diff,axiom,(
    ! [B_6: pname > $o,A_18: pname > $o,F_11: pname > hoare_1708887482_state,C_2: pname > $o] :
      ( ( inj_on1553129421_state @ F_11 @ C_2 )
     => ( ( ord_less_eq_pname_o @ A_18 @ C_2 )
       => ( ( ord_less_eq_pname_o @ B_6 @ C_2 )
         => ( ( image_1116629049_state @ F_11 @ ( minus_minus_pname_o @ A_18 @ B_6 ) )
            = ( minus_2056855718tate_o @ ( image_1116629049_state @ F_11 @ A_18 ) @ ( image_1116629049_state @ F_11 @ B_6 ) ) ) ) ) ) )).

thf(fact_1154_union__fold__insert,axiom,(
    ! [B_5: com > $o,A_17: com > $o] :
      ( ( finite_finite_com @ A_17 )
     => ( ( semila1562558655_com_o @ A_17 @ B_5 )
        = ( finite504235573_com_o @ insert_com @ B_5 @ A_17 ) ) ) )).

thf(fact_1155_union__fold__insert,axiom,(
    ! [B_5: pname > $o,A_17: pname > $o] :
      ( ( finite_finite_pname @ A_17 )
     => ( ( semila1780557381name_o @ A_17 @ B_5 )
        = ( finite603803317name_o @ insert_pname @ B_5 @ A_17 ) ) ) )).

thf(fact_1156_union__fold__insert,axiom,(
    ! [B_5: hoare_1708887482_state > $o,A_17: hoare_1708887482_state > $o] :
      ( ( finite1625599783_state @ A_17 )
     => ( ( semila1122118281tate_o @ A_17 @ B_5 )
        = ( finite96880613tate_o @ insert528405184_state @ B_5 @ A_17 ) ) ) )).

thf(fact_1157_union__fold__insert,axiom,(
    ! [B_5: ( pname > $o ) > $o,A_17: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_17 )
     => ( ( semila181081674me_o_o @ A_17 @ B_5 )
        = ( finite1849951719me_o_o @ insert_pname_o @ B_5 @ A_17 ) ) ) )).

thf(fact_1158_union__fold__insert,axiom,(
    ! [B_5: ( hoare_1708887482_state > $o ) > $o,A_17: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_17 )
     => ( ( semila1853742644te_o_o @ A_17 @ B_5 )
        = ( finite463603445te_o_o @ insert949073679tate_o @ B_5 @ A_17 ) ) ) )).

thf(fact_1159_dom__minus,axiom,(
    ! [A_16: pname > $o,F_10: pname > option_com,X_7: pname] :
      ( ( ( F_10 @ X_7 )
        = none_com )
     => ( ( minus_minus_pname_o @ ( dom_pname_com @ F_10 ) @ ( insert_pname @ X_7 @ A_16 ) )
        = ( minus_minus_pname_o @ ( dom_pname_com @ F_10 ) @ A_16 ) ) ) )).

thf(fact_1160_Sup__fin_Oidem,axiom,(
    ! [X_6: $o] :
      ( ( semila10642723_sup_o @ X_6 @ X_6 )
    <=> X_6 ) )).

thf(fact_1161_Sup__fin_Oidem,axiom,(
    ! [X_6: pname > $o] :
      ( ( semila1780557381name_o @ X_6 @ X_6 )
      = X_6 ) )).

thf(fact_1162_Sup__fin_Oidem,axiom,(
    ! [X_6: hoare_1708887482_state > $o] :
      ( ( semila1122118281tate_o @ X_6 @ X_6 )
      = X_6 ) )).

thf(fact_1163_folding__one_Oeq__fold_H,axiom,(
    ! [X_5: com,A_15: com > $o,F_9: com > com > com,F_8: ( com > $o ) > com] :
      ( ( finite860057415ne_com @ F_9 @ F_8 )
     => ( ( finite_finite_com @ A_15 )
       => ( ~ ( member_com @ X_5 @ A_15 )
         => ( ( F_8 @ ( insert_com @ X_5 @ A_15 ) )
            = ( finite_fold_com_com @ F_9 @ X_5 @ A_15 ) ) ) ) ) )).

thf(fact_1164_folding__one_Oeq__fold_H,axiom,(
    ! [X_5: pname,A_15: pname > $o,F_9: pname > pname > pname,F_8: ( pname > $o ) > pname] :
      ( ( finite1282449217_pname @ F_9 @ F_8 )
     => ( ( finite_finite_pname @ A_15 )
       => ( ~ ( member_pname @ X_5 @ A_15 )
         => ( ( F_8 @ ( insert_pname @ X_5 @ A_15 ) )
            = ( finite1657623752_pname @ F_9 @ X_5 @ A_15 ) ) ) ) ) )).

thf(fact_1165_folding__one_Oeq__fold_H,axiom,(
    ! [X_5: hoare_1708887482_state,A_15: hoare_1708887482_state > $o,F_9: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_8: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1615457021_state @ F_9 @ F_8 )
     => ( ( finite1625599783_state @ A_15 )
       => ( ~ ( member451959335_state @ X_5 @ A_15 )
         => ( ( F_8 @ ( insert528405184_state @ X_5 @ A_15 ) )
            = ( finite309095018_state @ F_9 @ X_5 @ A_15 ) ) ) ) ) )).

thf(fact_1166_folding__one_Oeq__fold_H,axiom,(
    ! [X_5: pname > $o,A_15: ( pname > $o ) > $o,F_9: ( pname > $o ) > ( pname > $o ) > pname > $o,F_8: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite349908348name_o @ F_9 @ F_8 )
     => ( ( finite297249702name_o @ A_15 )
       => ( ~ ( member_pname_o @ X_5 @ A_15 )
         => ( ( F_8 @ ( insert_pname_o @ X_5 @ A_15 ) )
            = ( finite472615016name_o @ F_9 @ X_5 @ A_15 ) ) ) ) ) )).

thf(fact_1167_folding__one_Oeq__fold_H,axiom,(
    ! [X_5: hoare_1708887482_state > $o,A_15: ( hoare_1708887482_state > $o ) > $o,F_9: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_8: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite928843026tate_o @ F_9 @ F_8 )
     => ( ( finite1329924456tate_o @ A_15 )
       => ( ~ ( member814030440tate_o @ X_5 @ A_15 )
         => ( ( F_8 @ ( insert949073679tate_o @ X_5 @ A_15 ) )
            = ( finite822533768tate_o @ F_9 @ X_5 @ A_15 ) ) ) ) ) )).

thf(fact_1168_folding__one__idem_Oeq__fold__idem_H,axiom,(
    ! [A_14: com,A_13: com > $o,F_7: com > com > com,F_6: ( com > $o ) > com] :
      ( ( finite666746948em_com @ F_7 @ F_6 )
     => ( ( finite_finite_com @ A_13 )
       => ( ( F_6 @ ( insert_com @ A_14 @ A_13 ) )
          = ( finite_fold_com_com @ F_7 @ A_14 @ A_13 ) ) ) ) )).

thf(fact_1169_folding__one__idem_Oeq__fold__idem_H,axiom,(
    ! [A_14: pname,A_13: pname > $o,F_7: pname > pname > pname,F_6: ( pname > $o ) > pname] :
      ( ( finite89670078_pname @ F_7 @ F_6 )
     => ( ( finite_finite_pname @ A_13 )
       => ( ( F_6 @ ( insert_pname @ A_14 @ A_13 ) )
          = ( finite1657623752_pname @ F_7 @ A_14 @ A_13 ) ) ) ) )).

thf(fact_1170_folding__one__idem_Oeq__fold__idem_H,axiom,(
    ! [A_14: hoare_1708887482_state,A_13: hoare_1708887482_state > $o,F_7: hoare_1708887482_state > hoare_1708887482_state > hoare_1708887482_state,F_6: ( hoare_1708887482_state > $o ) > hoare_1708887482_state] :
      ( ( finite1347568576_state @ F_7 @ F_6 )
     => ( ( finite1625599783_state @ A_13 )
       => ( ( F_6 @ ( insert528405184_state @ A_14 @ A_13 ) )
          = ( finite309095018_state @ F_7 @ A_14 @ A_13 ) ) ) ) )).

thf(fact_1171_folding__one__idem_Oeq__fold__idem_H,axiom,(
    ! [A_14: pname > $o,A_13: ( pname > $o ) > $o,F_7: ( pname > $o ) > ( pname > $o ) > pname > $o,F_6: ( ( pname > $o ) > $o ) > pname > $o] :
      ( ( finite697516351name_o @ F_7 @ F_6 )
     => ( ( finite297249702name_o @ A_13 )
       => ( ( F_6 @ ( insert_pname_o @ A_14 @ A_13 ) )
          = ( finite472615016name_o @ F_7 @ A_14 @ A_13 ) ) ) ) )).

thf(fact_1172_folding__one__idem_Oeq__fold__idem_H,axiom,(
    ! [A_14: hoare_1708887482_state > $o,A_13: ( hoare_1708887482_state > $o ) > $o,F_7: ( hoare_1708887482_state > $o ) > ( hoare_1708887482_state > $o ) > hoare_1708887482_state > $o,F_6: ( ( hoare_1708887482_state > $o ) > $o ) > hoare_1708887482_state > $o] :
      ( ( finite621643279tate_o @ F_7 @ F_6 )
     => ( ( finite1329924456tate_o @ A_13 )
       => ( ( F_6 @ ( insert949073679tate_o @ A_14 @ A_13 ) )
          = ( finite822533768tate_o @ F_7 @ A_14 @ A_13 ) ) ) ) )).

thf(fact_1173_WT_OBody,axiom,(
    ! [Pn_1: pname] :
      ( ( ( body @ Pn_1 )
       != none_com )
     => ( wt @ ( body_1 @ Pn_1 ) ) ) )).

thf(fact_1174_inj__on__insert,axiom,(
    ! [F_5: pname > hoare_1708887482_state,A_12: pname,A_11: pname > $o] :
      ( ( inj_on1553129421_state @ F_5 @ ( insert_pname @ A_12 @ A_11 ) )
    <=> ( ( inj_on1553129421_state @ F_5 @ A_11 )
        & ~ ( member451959335_state @ ( F_5 @ A_12 ) @ ( image_1116629049_state @ F_5 @ ( minus_minus_pname_o @ A_11 @ ( insert_pname @ A_12 @ bot_bot_pname_o ) ) ) ) ) ) )).

thf(fact_1175_dom__fun__upd,axiom,(
    ! [F_4: pname > option_com,X_4: pname,Y_2: option_com] :
      ( ( ( Y_2 = none_com )
       => ( ( dom_pname_com @ ( fun_up879233478on_com @ F_4 @ X_4 @ Y_2 ) )
          = ( minus_minus_pname_o @ ( dom_pname_com @ F_4 ) @ ( insert_pname @ X_4 @ bot_bot_pname_o ) ) ) )
      & ( ( Y_2 != none_com )
       => ( ( dom_pname_com @ ( fun_up879233478on_com @ F_4 @ X_4 @ Y_2 ) )
          = ( insert_pname @ X_4 @ ( dom_pname_com @ F_4 ) ) ) ) ) )).

thf(fact_1176_inf__le__fold__inf,axiom,(
    ! [C_1: pname > $o,B_4: pname > $o,A_10: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_10 )
     => ( ! [X_3: pname > $o] :
            ( ( member_pname_o @ X_3 @ A_10 )
           => ( ord_less_eq_pname_o @ B_4 @ X_3 ) )
       => ( ord_less_eq_pname_o @ ( semila1673364395name_o @ B_4 @ C_1 ) @ ( finite472615016name_o @ semila1673364395name_o @ C_1 @ A_10 ) ) ) ) )).

thf(fact_1177_inf__le__fold__inf,axiom,(
    ! [C_1: hoare_1708887482_state > $o,B_4: hoare_1708887482_state > $o,A_10: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_10 )
     => ( ! [X_3: hoare_1708887482_state > $o] :
            ( ( member814030440tate_o @ X_3 @ A_10 )
           => ( ord_le777019615tate_o @ B_4 @ X_3 ) )
       => ( ord_le777019615tate_o @ ( semila129691299tate_o @ B_4 @ C_1 ) @ ( finite822533768tate_o @ semila129691299tate_o @ C_1 @ A_10 ) ) ) ) )).

thf(fact_1178_inf__le__fold__inf,axiom,(
    ! [C_1: $o,B_4: $o,A_10: $o > $o] :
      ( ( finite_finite_o @ A_10 )
     => ( ! [X_3: $o] :
            ( ( member_o @ X_3 @ A_10 )
           => ( ord_less_eq_o @ B_4 @ X_3 ) )
       => ( ord_less_eq_o @ ( semila854092349_inf_o @ B_4 @ C_1 ) @ ( finite_fold_o_o @ semila854092349_inf_o @ C_1 @ A_10 ) ) ) ) )).

thf(fact_1179_fold__sup__le__sup,axiom,(
    ! [C: pname > $o,B_3: pname > $o,A_9: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_9 )
     => ( ! [X_3: pname > $o] :
            ( ( member_pname_o @ X_3 @ A_9 )
           => ( ord_less_eq_pname_o @ X_3 @ B_3 ) )
       => ( ord_less_eq_pname_o @ ( finite472615016name_o @ semila1780557381name_o @ C @ A_9 ) @ ( semila1780557381name_o @ B_3 @ C ) ) ) ) )).

thf(fact_1180_fold__sup__le__sup,axiom,(
    ! [C: hoare_1708887482_state > $o,B_3: hoare_1708887482_state > $o,A_9: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_9 )
     => ( ! [X_3: hoare_1708887482_state > $o] :
            ( ( member814030440tate_o @ X_3 @ A_9 )
           => ( ord_le777019615tate_o @ X_3 @ B_3 ) )
       => ( ord_le777019615tate_o @ ( finite822533768tate_o @ semila1122118281tate_o @ C @ A_9 ) @ ( semila1122118281tate_o @ B_3 @ C ) ) ) ) )).

thf(fact_1181_fold__sup__le__sup,axiom,(
    ! [C: $o,B_3: $o,A_9: $o > $o] :
      ( ( finite_finite_o @ A_9 )
     => ( ! [X_3: $o] :
            ( ( member_o @ X_3 @ A_9 )
           => ( ord_less_eq_o @ X_3 @ B_3 ) )
       => ( ord_less_eq_o @ ( finite_fold_o_o @ semila10642723_sup_o @ C @ A_9 ) @ ( semila10642723_sup_o @ B_3 @ C ) ) ) ) )).

thf(fact_1182_inj__on__iff__surj,axiom,(
    ! [A_8: pname > $o,A_7: hoare_1708887482_state > $o] :
      ( ( A_7 != bot_bo19817387tate_o )
     => ( ? [F_3: hoare_1708887482_state > pname] :
            ( ( inj_on1945914667_pname @ F_3 @ A_7 )
            & ( ord_less_eq_pname_o @ ( image_1509414295_pname @ F_3 @ A_7 ) @ A_8 ) )
      <=> ? [G_1: pname > hoare_1708887482_state] :
            ( ( image_1116629049_state @ G_1 @ A_8 )
            = A_7 ) ) ) )).

thf(fact_1183_inj__on__iff__surj,axiom,(
    ! [A_8: hoare_1708887482_state > $o,A_7: pname > $o] :
      ( ( A_7 != bot_bot_pname_o )
     => ( ? [F_3: pname > hoare_1708887482_state] :
            ( ( inj_on1553129421_state @ F_3 @ A_7 )
            & ( ord_le777019615tate_o @ ( image_1116629049_state @ F_3 @ A_7 ) @ A_8 ) )
      <=> ? [G_1: hoare_1708887482_state > pname] :
            ( ( image_1509414295_pname @ G_1 @ A_8 )
            = A_7 ) ) ) )).

thf(fact_1184_option_Oexhaust,axiom,(
    ! [Y_1: option_com] :
      ( ( Y_1 != none_com )
     => ~ ! [A_6: com] :
            ( Y_1
           != ( some_com @ A_6 ) ) ) )).

thf(fact_1185_option_Oexhaust,axiom,(
    ! [Y_1: option_pname] :
      ( ( Y_1 != none_pname )
     => ~ ! [A_6: pname] :
            ( Y_1
           != ( some_pname @ A_6 ) ) ) )).

thf(fact_1186_option_Oexhaust,axiom,(
    ! [Y_1: option1624383643_state] :
      ( ( Y_1 != none_H1106584047_state )
     => ~ ! [A_6: hoare_1708887482_state] :
            ( Y_1
           != ( some_H1974565227_state @ A_6 ) ) ) )).

thf(fact_1187_Cantor__Bernstein__aux,axiom,(
    ! [G: hoare_1708887482_state > pname,B_2: hoare_1708887482_state > $o,F_2: pname > hoare_1708887482_state,A_4: pname > $o] :
    ? [A_5: pname > $o] :
      ( ( ord_less_eq_pname_o @ A_5 @ A_4 )
      & ! [X_3: pname] :
          ( ( member_pname @ X_3 @ A_5 )
         => ~ ( member_pname @ X_3 @ ( image_1509414295_pname @ G @ ( minus_2056855718tate_o @ B_2 @ ( image_1116629049_state @ F_2 @ A_5 ) ) ) ) )
      & ? [H: pname > hoare_1708887482_state] :
          ( ! [X_3: pname] :
              ( ( member_pname @ X_3 @ A_5 )
             => ( ( H @ X_3 )
                = ( F_2 @ X_3 ) ) )
          & ! [X_3: pname] :
              ( ( member_pname @ X_3 @ ( minus_minus_pname_o @ A_4 @ A_5 ) )
             => ( ( member451959335_state @ ( H @ X_3 ) @ ( minus_2056855718tate_o @ B_2 @ ( image_1116629049_state @ F_2 @ A_5 ) ) )
                & ( X_3
                  = ( G @ ( H @ X_3 ) ) ) ) ) ) ) )).

thf(fact_1188_Cantor__Bernstein__aux,axiom,(
    ! [G: pname > hoare_1708887482_state,B_2: pname > $o,F_2: hoare_1708887482_state > pname,A_4: hoare_1708887482_state > $o] :
    ? [A_5: hoare_1708887482_state > $o] :
      ( ( ord_le777019615tate_o @ A_5 @ A_4 )
      & ! [X_3: hoare_1708887482_state] :
          ( ( member451959335_state @ X_3 @ A_5 )
         => ~ ( member451959335_state @ X_3 @ ( image_1116629049_state @ G @ ( minus_minus_pname_o @ B_2 @ ( image_1509414295_pname @ F_2 @ A_5 ) ) ) ) )
      & ? [H: hoare_1708887482_state > pname] :
          ( ! [X_3: hoare_1708887482_state] :
              ( ( member451959335_state @ X_3 @ A_5 )
             => ( ( H @ X_3 )
                = ( F_2 @ X_3 ) ) )
          & ! [X_3: hoare_1708887482_state] :
              ( ( member451959335_state @ X_3 @ ( minus_2056855718tate_o @ A_4 @ A_5 ) )
             => ( ( member_pname @ ( H @ X_3 ) @ ( minus_minus_pname_o @ B_2 @ ( image_1509414295_pname @ F_2 @ A_5 ) ) )
                & ( X_3
                  = ( G @ ( H @ X_3 ) ) ) ) ) ) ) )).

thf(fact_1189_image__vimage__subset,axiom,(
    ! [F_1: pname > hoare_1708887482_state,A_3: hoare_1708887482_state > $o] :
      ( ord_le777019615tate_o @ ( image_1116629049_state @ F_1 @ ( vimage1943311875_state @ F_1 @ A_3 ) ) @ A_3 ) )).

thf(fact_1190_dom__restrict,axiom,(
    ! [M: pname > option_com,A_2: pname > $o] :
      ( ( dom_pname_com @ ( restri1382200118me_com @ M @ A_2 ) )
      = ( semila1673364395name_o @ ( dom_pname_com @ M ) @ A_2 ) ) )).

thf(fact_1191_Inf__fin_Ounion__disjoint,axiom,(
    ! [B_1: ( pname > $o ) > $o,A_1: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A_1 )
     => ( ( A_1 != bot_bot_pname_o_o )
       => ( ( finite297249702name_o @ B_1 )
         => ( ( B_1 != bot_bot_pname_o_o )
           => ( ( ( semila2013987940me_o_o @ A_1 @ B_1 )
                = bot_bot_pname_o_o )
             => ( ( big_la1126801287name_o @ ( semila181081674me_o_o @ A_1 @ B_1 ) )
                = ( semila1673364395name_o @ ( big_la1126801287name_o @ A_1 ) @ ( big_la1126801287name_o @ B_1 ) ) ) ) ) ) ) ) )).

thf(fact_1192_Inf__fin_Ounion__disjoint,axiom,(
    ! [B_1: ( hoare_1708887482_state > $o ) > $o,A_1: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A_1 )
     => ( ( A_1 != bot_bo1678742418te_o_o )
       => ( ( finite1329924456tate_o @ B_1 )
         => ( ( B_1 != bot_bo1678742418te_o_o )
           => ( ( ( semila598060698te_o_o @ A_1 @ B_1 )
                = bot_bo1678742418te_o_o )
             => ( ( big_la781588935tate_o @ ( semila1853742644te_o_o @ A_1 @ B_1 ) )
                = ( semila129691299tate_o @ ( big_la781588935tate_o @ A_1 ) @ ( big_la781588935tate_o @ B_1 ) ) ) ) ) ) ) ) )).

thf(fact_1193_Inf__fin_Ounion__inter,axiom,(
    ! [B: ( pname > $o ) > $o,A: ( pname > $o ) > $o] :
      ( ( finite297249702name_o @ A )
     => ( ( finite297249702name_o @ B )
       => ( ( ( semila2013987940me_o_o @ A @ B )
           != bot_bot_pname_o_o )
         => ( ( semila1673364395name_o @ ( big_la1126801287name_o @ ( semila181081674me_o_o @ A @ B ) ) @ ( big_la1126801287name_o @ ( semila2013987940me_o_o @ A @ B ) ) )
            = ( semila1673364395name_o @ ( big_la1126801287name_o @ A ) @ ( big_la1126801287name_o @ B ) ) ) ) ) ) )).

thf(fact_1194_Inf__fin_Ounion__inter,axiom,(
    ! [B: ( hoare_1708887482_state > $o ) > $o,A: ( hoare_1708887482_state > $o ) > $o] :
      ( ( finite1329924456tate_o @ A )
     => ( ( finite1329924456tate_o @ B )
       => ( ( ( semila598060698te_o_o @ A @ B )
           != bot_bo1678742418te_o_o )
         => ( ( semila129691299tate_o @ ( big_la781588935tate_o @ ( semila1853742644te_o_o @ A @ B ) ) @ ( big_la781588935tate_o @ ( semila598060698te_o_o @ A @ B ) ) )
            = ( semila129691299tate_o @ ( big_la781588935tate_o @ A ) @ ( big_la781588935tate_o @ B ) ) ) ) ) ) )).

thf(fact_1195_UNIV__I,axiom,(
    ! [X_2: com] :
      ( member_com @ X_2 @ top_top_com_o ) )).

thf(fact_1196_UNIV__I,axiom,(
    ! [X_2: pname] :
      ( member_pname @ X_2 @ top_top_pname_o ) )).

thf(fact_1197_UNIV__I,axiom,(
    ! [X_2: hoare_1708887482_state] :
      ( member451959335_state @ X_2 @ top_to832624271tate_o ) )).

thf(fact_1198_rangeI,axiom,(
    ! [F: pname > hoare_1708887482_state,X_1: pname] :
      ( member451959335_state @ ( F @ X_1 ) @ ( image_1116629049_state @ F @ top_top_pname_o ) ) )).

%----Helper facts (18)
thf(help_fequal_1_1_fequal_000tc__Com__Ocom_T,axiom,(
    ! [X: com,Y: com] :
      ( ~ ( fequal_com @ X @ Y )
      | ( X = Y ) ) )).

thf(help_fequal_2_1_fequal_000tc__Com__Ocom_T,axiom,(
    ! [X: com,Y: com] :
      ( ( X != Y )
      | ( fequal_com @ X @ Y ) ) )).

thf(help_fequal_1_1_fequal_000tc__Com__Opname_T,axiom,(
    ! [X: pname,Y: pname] :
      ( ~ ( fequal_pname @ X @ Y )
      | ( X = Y ) ) )).

thf(help_fequal_2_1_fequal_000tc__Com__Opname_T,axiom,(
    ! [X: pname,Y: pname] :
      ( ( X != Y )
      | ( fequal_pname @ X @ Y ) ) )).

thf(help_fequal_1_1_fequal_000tc__Com__Ostate_T,axiom,(
    ! [X: state,Y: state] :
      ( ~ ( fequal_state @ X @ Y )
      | ( X = Y ) ) )).

thf(help_fequal_2_1_fequal_000tc__Com__Ostate_T,axiom,(
    ! [X: state,Y: state] :
      ( ( X != Y )
      | ( fequal_state @ X @ Y ) ) )).

thf(help_fequal_1_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,(
    ! [X: pname > $o,Y: pname > $o] :
      ( ~ ( fequal_pname_o @ X @ Y )
      | ( X = Y ) ) )).

thf(help_fequal_2_1_fequal_000_062_Itc__Com__Opname_M_Eo_J_T,axiom,(
    ! [X: pname > $o,Y: pname > $o] :
      ( ( X != Y )
      | ( fequal_pname_o @ X @ Y ) ) )).

thf(help_If_1_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,(
    ! [X: option_com,Y: option_com] :
      ( ( if_option_com @ $true @ X @ Y )
      = X ) )).

thf(help_If_2_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,(
    ! [X: option_com,Y: option_com] :
      ( ( if_option_com @ $false @ X @ Y )
      = Y ) )).

thf(help_If_3_1_If_000tc__Option__Ooption_Itc__Com__Ocom_J_T,axiom,(
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) )).

thf(help_If_1_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate,axiom,(
    ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
      ( ( if_Hoa1374726218_state @ $true @ X @ Y )
      = X ) )).

thf(help_If_2_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate,axiom,(
    ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
      ( ( if_Hoa1374726218_state @ $false @ X @ Y )
      = Y ) )).

thf(help_If_3_1_If_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com__Ostate,axiom,(
    ! [P: $o] :
      ( ( P = $true )
      | ( P = $false ) ) )).

thf(help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,axiom,(
    ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
      ( ~ ( fequal224822779_state @ X @ Y )
      | ( X = Y ) ) )).

thf(help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_Itc__Com,axiom,(
    ! [X: hoare_1708887482_state,Y: hoare_1708887482_state] :
      ( ( X != Y )
      | ( fequal224822779_state @ X @ Y ) ) )).

thf(help_fequal_1_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,axiom,(
    ! [X: hoare_1708887482_state > $o,Y: hoare_1708887482_state > $o] :
      ( ~ ( fequal1436017556tate_o @ X @ Y )
      | ( X = Y ) ) )).

thf(help_fequal_2_1_fequal_000_062_Itc__Hoare____Mirabelle____nqhfsdfvyv__Otriple_It,axiom,(
    ! [X: hoare_1708887482_state > $o,Y: hoare_1708887482_state > $o] :
      ( ( X != Y )
      | ( fequal1436017556tate_o @ X @ Y ) ) )).

%----Conjectures (8)
thf(conj_0,hypothesis,(
    hoare_1160767572gleton )).

thf(conj_1,hypothesis,(
    wT_bodies )).

thf(conj_2,hypothesis,
    ( finite1625599783_state @ fa )).

thf(conj_3,hypothesis,(
    ~ ( member451959335_state @ ( hoare_Mirabelle_MGT @ y ) @ fa ) )).

thf(conj_4,hypothesis,
    ( ord_le777019615tate_o @ fa
    @ ( image_1116629049_state
      @ ^ [Pn: pname] :
          ( hoare_Mirabelle_MGT @ ( the_com @ ( body @ Pn ) ) )
      @ ( dom_pname_com @ body ) ) )).

thf(conj_5,hypothesis,
    ( ( body @ pn )
    = ( some_com @ y ) )).

thf(conj_6,hypothesis,
    ( hoare_90032982_state
    @ ( image_1116629049_state
      @ ^ [Pn: pname] :
          ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
      @ ( dom_pname_com @ body ) )
    @ fa )).

thf(conj_7,conjecture,
    ( hoare_90032982_state
    @ ( image_1116629049_state
      @ ^ [Pn: pname] :
          ( hoare_Mirabelle_MGT @ ( body_1 @ Pn ) )
      @ ( dom_pname_com @ body ) )
    @ ( insert528405184_state @ ( hoare_Mirabelle_MGT @ y ) @ bot_bo19817387tate_o ) )).

%------------------------------------------------------------------------------