% Mizar ND problem: t1_amistd_1,amistd_1,44,38 
fof(dh_c1_1__amistd_1,definition,
    ( ( v1_xreal_0(c1_1__amistd_1)
     => k1_pre_circ(k1_tarski(c1_1__amistd_1)) = c1_1__amistd_1 )
   => ! [A] : 
        ( v1_xreal_0(A)
       => k1_pre_circ(k1_tarski(A)) = A ) ),
    introduced(definition,[new_symbol(c1_1__amistd_1),file(amistd_1,c1_1__amistd_1)]),
    [interesting(0.8),axiom,file(amistd_1,c1_1__amistd_1)]).

fof(cc1_funct_7,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A)
        & v1_funct_7(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_finseq_1(A)
        & v1_funcop_1(A) ) ) ),
    file(funct_7,cc1_funct_7),
    [interesting(0.9),axiom,file(funct_7,cc1_funct_7)]).

fof(t2_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    [interesting(0.9),axiom,file(real,t2_real)]).

fof(t3_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    [interesting(0.9),axiom,file(real,t3_real)]).

fof(cc1_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) ) ) ),
    file(finseq_1,cc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,cc1_finseq_1)]).

fof(cc2_funct_7,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A)
        & v1_finseq_1(A)
        & v1_funcop_1(A)
        & v1_funct_7(A) ) ) ),
    file(funct_7,cc2_funct_7),
    [interesting(0.9),axiom,file(funct_7,cc2_funct_7)]).

fof(cc3_int_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_int_1(A) ) ),
    file(int_1,cc3_int_1),
    [interesting(0.9),axiom,file(int_1,cc3_int_1)]).

fof(cc3_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc3_nat_1)]).

fof(cc4_int_1,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    [interesting(0.9),axiom,file(int_1,cc4_int_1)]).

fof(fc10_membered,theorem,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A)) ) ) ),
    file(membered,fc10_membered),
    [interesting(0.9),axiom,file(membered,fc10_membered)]).

fof(fc11_membered,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A))
        & v4_membered(k1_tarski(A))
        & v5_membered(k1_tarski(A)) ) ) ),
    file(membered,fc11_membered),
    [interesting(0.9),axiom,file(membered,fc11_membered)]).

fof(fc7_membered,theorem,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_membered(k1_tarski(A)) ) ),
    file(membered,fc7_membered),
    [interesting(0.9),axiom,file(membered,fc7_membered)]).

fof(fc9_membered,theorem,(
    ! [A] : 
      ( v1_rat_1(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A))
        & v3_membered(k1_tarski(A)) ) ) ),
    file(membered,fc9_membered),
    [interesting(0.9),axiom,file(membered,fc9_membered)]).

fof(rc1_finseq_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc1_finseq_1)]).

fof(rc1_finseq_5,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_5,rc1_finseq_5),
    [interesting(0.9),axiom,file(finseq_5,rc1_finseq_5)]).

fof(rc1_nat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc1_nat_1)]).

fof(rc1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_xboole_0(A) ) ),
    file(partfun1,rc1_partfun1),
    [interesting(0.9),axiom,file(partfun1,rc1_partfun1)]).

fof(rc2_int_1,theorem,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    [interesting(0.9),axiom,file(int_1,rc2_int_1)]).

fof(rc3_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc3_finseq_1)]).

fof(rc3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A) ) ),
    file(funct_1,rc3_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc3_funct_1)]).

fof(rc3_relat_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A) ) ),
    file(relat_1,rc3_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc3_relat_1)]).

fof(rc4_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v3_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc4_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc4_funct_1)]).

fof(rc6_finseq_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v2_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc6_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc6_finseq_1)]).

fof(rc8_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A)
      & v1_finseq_1(A) ) ),
    file(finseq_1,rc8_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc8_finseq_1)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(dt_k2_seq_4,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_xreal_0(k2_seq_4(A)) ) ),
    file(seq_4,k2_seq_4),
    [interesting(0.9),axiom,file(seq_4,k2_seq_4)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(cc10_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    [interesting(0.9),axiom,file(membered,cc10_membered)]).

fof(cc11_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    [interesting(0.9),axiom,file(membered,cc11_membered)]).

fof(cc12_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    [interesting(0.9),axiom,file(membered,cc12_membered)]).

fof(cc13_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    [interesting(0.9),axiom,file(membered,cc13_membered)]).

fof(cc14_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    [interesting(0.9),axiom,file(membered,cc14_membered)]).

fof(cc1_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    [interesting(0.9),axiom,file(membered,cc1_membered)]).

fof(cc1_realset1,theorem,(
    ! [A] : 
      ( ~ v1_realset1(A)
     => ~ v1_xboole_0(A) ) ),
    file(realset1,cc1_realset1),
    [interesting(0.9),axiom,file(realset1,cc1_realset1)]).

fof(cc1_setfam_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_setfam_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ~ v1_xboole_0(B) ) ) ),
    file(setfam_1,cc1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,cc1_setfam_1)]).

fof(cc2_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_xboole_0(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(A)
        & v1_funct_1(A)
        & v2_funct_1(A) ) ) ),
    file(funct_1,cc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc2_funct_1)]).

fof(cc2_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    [interesting(0.9),axiom,file(membered,cc2_membered)]).

fof(cc3_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    [interesting(0.9),axiom,file(membered,cc3_membered)]).

fof(fc12_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0) ),
    file(relat_1,fc12_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc12_relat_1)]).

fof(fc1_pre_circ,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v5_membered(A) )
     => ( v4_ordinal2(k2_seq_4(A))
        & v1_xcmplx_0(k2_seq_4(A))
        & v1_xreal_0(k2_seq_4(A)) ) ) ),
    file(pre_circ,fc1_pre_circ),
    [interesting(0.9),axiom,file(pre_circ,fc1_pre_circ)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(fc2_finseq_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0) ),
    file(finseq_1,fc2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc2_finseq_1)]).

fof(fc3_funct_7,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0)
    & v3_relat_1(k1_xboole_0)
    & v1_funct_1(k1_xboole_0)
    & v2_funct_1(k1_xboole_0)
    & v1_finset_1(k1_xboole_0)
    & v1_finseq_1(k1_xboole_0)
    & v1_funcop_1(k1_xboole_0) ),
    file(funct_7,fc3_funct_7),
    [interesting(0.9),axiom,file(funct_7,fc3_funct_7)]).

fof(fc4_relat_1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_relat_1(k1_xboole_0) ),
    file(relat_1,fc4_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc4_relat_1)]).

fof(fc6_membered,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_membered(k1_xboole_0)
    & v2_membered(k1_xboole_0)
    & v3_membered(k1_xboole_0)
    & v4_membered(k1_xboole_0)
    & v5_membered(k1_xboole_0) ),
    file(membered,fc6_membered),
    [interesting(0.9),axiom,file(membered,fc6_membered)]).

fof(rc1_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc1_funct_1)]).

fof(rc1_membered,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    [interesting(0.9),axiom,file(membered,rc1_membered)]).

fof(rc1_pre_circ,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(pre_circ,rc1_pre_circ),
    [interesting(0.9),axiom,file(pre_circ,rc1_pre_circ)]).

fof(rc1_realset1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_realset1(A) ) ),
    file(realset1,rc1_realset1),
    [interesting(0.9),axiom,file(realset1,rc1_realset1)]).

fof(rc1_relat_1,theorem,(
    ? [A] : 
      ( v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc1_relat_1)]).

fof(rc1_setfam_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_setfam_1(A) ) ),
    file(setfam_1,rc1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,rc1_setfam_1)]).

fof(rc2_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_xboole_0(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc2_funct_1),
    [interesting(0.9),axiom,file(funct_1,rc2_funct_1)]).

fof(rc2_realset1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & ~ v1_realset1(A) ) ),
    file(realset1,rc2_realset1),
    [interesting(0.9),axiom,file(realset1,rc2_realset1)]).

fof(rc2_relat_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A) ) ),
    file(relat_1,rc2_relat_1),
    [interesting(0.9),axiom,file(relat_1,rc2_relat_1)]).

fof(rc7_finseq_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_relat_1(A)
      & v1_funct_1(A)
      & v1_finset_1(A) ) ),
    file(finseq_1,rc7_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,rc7_finseq_1)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(reflexivity_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(connectedness_r1_xreal_0,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    [interesting(0.9),axiom,file(xreal_0,r1_xreal_0)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(redefinition_k1_pre_circ,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v2_membered(A) )
     => k1_pre_circ(A) = k2_seq_4(A) ) ),
    file(pre_circ,k1_pre_circ),
    [interesting(0.9),axiom,file(pre_circ,k1_pre_circ)]).

fof(dt_k1_pre_circ,axiom,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v2_membered(A) )
     => v1_xreal_0(k1_pre_circ(A)) ) ),
    file(pre_circ,k1_pre_circ),
    [interesting(0.9),axiom,file(pre_circ,k1_pre_circ)]).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    [interesting(0.9),axiom,file(tarski,k1_tarski)]).

fof(dt_c1_1__amistd_1,assumption,(
    v1_xreal_0(c1_1__amistd_1) ),
    introduced(assumption,[file(amistd_1,c1_1__amistd_1)]),
    [interesting(0.8),axiom,file(amistd_1,c1_1__amistd_1)]).

fof(cc15_membered,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    [interesting(0.9),axiom,file(membered,cc15_membered)]).

fof(cc1_finseq_5,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_realset1(A) ) ),
    file(finseq_5,cc1_finseq_5),
    [interesting(0.9),axiom,file(finseq_5,cc1_finseq_5)]).

fof(cc1_finset_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_finset_1(A) ) ),
    file(finset_1,cc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,cc1_finset_1)]).

fof(cc1_funct_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_funct_1(A) ) ),
    file(funct_1,cc1_funct_1),
    [interesting(0.9),axiom,file(funct_1,cc1_funct_1)]).

fof(cc1_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => v1_relat_1(A) ) ),
    file(relat_1,cc1_relat_1),
    [interesting(0.9),axiom,file(relat_1,cc1_relat_1)]).

fof(cc1_scmring1,theorem,(
    ! [A] : 
      ( ~ v1_finset_1(A)
     => ( ~ v1_xboole_0(A)
        & ~ v1_realset1(A) ) ) ),
    file(scmring1,cc1_scmring1),
    [interesting(0.9),axiom,file(scmring1,cc1_scmring1)]).

fof(cc4_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    [interesting(0.9),axiom,file(membered,cc4_membered)]).

fof(fc1_finset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A)) ) ),
    file(finset_1,fc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,fc1_finset_1)]).

fof(fc2_setfam_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_setfam_1(k1_tarski(A)) ) ) ),
    file(setfam_1,fc2_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,fc2_setfam_1)]).

fof(fc2_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc2_subset_1)]).

fof(fc3_realset1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k1_tarski(A))
      & v1_finset_1(k1_tarski(A))
      & v1_realset1(k1_tarski(A)) ) ),
    file(realset1,fc3_realset1),
    [interesting(0.9),axiom,file(realset1,fc3_realset1)]).

fof(fc8_membered,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_membered(k1_tarski(A))
        & v2_membered(k1_tarski(A)) ) ) ),
    file(membered,fc8_membered),
    [interesting(0.9),axiom,file(membered,fc8_membered)]).

fof(rc1_finset_1,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_finset_1(A) ) ),
    file(finset_1,rc1_finset_1),
    [interesting(0.9),axiom,file(finset_1,rc1_finset_1)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.9),axiom,file(tarski,d1_tarski)]).

fof(e1_1__amistd_1,plain,
    ( r2_hidden(c1_1__amistd_1,k1_tarski(c1_1__amistd_1))
    & ! [A] : 
        ( v1_xreal_0(A)
       => ( r2_hidden(A,k1_tarski(c1_1__amistd_1))
         => r1_xreal_0(A,c1_1__amistd_1) ) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__amistd_1])],[cc1_funct_7,t2_real,t3_real,cc1_finseq_1,cc2_funct_7,cc3_int_1,cc3_nat_1,cc4_int_1,fc10_membered,fc11_membered,fc9_membered,rc1_finseq_1,rc1_finseq_5,rc1_nat_1,rc1_partfun1,rc2_int_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,dt_k1_xboole_0,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_setfam_1,cc2_funct_1,cc2_membered,cc3_membered,fc12_relat_1,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc6_membered,fc7_membered,rc1_funct_1,rc1_membered,rc1_pre_circ,rc1_relat_1,rc1_setfam_1,rc2_funct_1,rc2_relat_1,rc7_finseq_1,existence_m1_subset_1,dt_m1_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_realset1,cc1_relat_1,cc1_scmring1,cc4_membered,fc2_setfam_1,rc1_finset_1,rc1_realset1,rc1_xboole_0,rc2_realset1,rc2_xboole_0,t2_subset,t6_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,dt_k1_tarski,dt_c1_1__amistd_1,fc1_finset_1,fc2_subset_1,fc3_realset1,fc8_membered,t1_subset,t7_boole,d1_tarski]),
    [interesting(0.8),file(amistd_1,e1_1__amistd_1),[file(amistd_1,e1_1__amistd_1)]]).

fof(d1_pre_circ,definition,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_finset_1(A)
        & v2_membered(A) )
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( B = k1_pre_circ(A)
          <=> ( r2_hidden(B,A)
              & ! [C] : 
                  ( v1_xreal_0(C)
                 => ( r2_hidden(C,A)
                   => r1_xreal_0(C,B) ) ) ) ) ) ) ),
    file(pre_circ,d1_pre_circ),
    [interesting(0.9),axiom,file(pre_circ,d1_pre_circ)]).

fof(e2_1__amistd_1,plain,(
    k1_pre_circ(k1_tarski(c1_1__amistd_1)) = c1_1__amistd_1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_1__amistd_1])],[cc1_funct_7,t2_real,t3_real,cc1_finseq_1,cc2_funct_7,cc3_int_1,cc3_nat_1,cc4_int_1,fc10_membered,fc11_membered,fc7_membered,fc9_membered,rc1_finseq_1,rc1_finseq_5,rc1_nat_1,rc1_partfun1,rc2_int_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc8_finseq_1,existence_m1_subset_1,dt_k1_xboole_0,dt_k2_seq_4,dt_m1_subset_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc1_membered,cc1_realset1,cc1_setfam_1,cc2_funct_1,cc2_membered,cc3_membered,fc12_relat_1,fc1_pre_circ,fc1_xboole_0,fc2_finseq_1,fc3_funct_7,fc4_relat_1,fc6_membered,rc1_funct_1,rc1_membered,rc1_pre_circ,rc1_realset1,rc1_relat_1,rc1_setfam_1,rc2_funct_1,rc2_realset1,rc2_relat_1,rc7_finseq_1,t2_subset,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k1_pre_circ,dt_k1_pre_circ,dt_k1_tarski,dt_c1_1__amistd_1,cc15_membered,cc1_finseq_5,cc1_finset_1,cc1_funct_1,cc1_relat_1,cc1_scmring1,cc4_membered,fc1_finset_1,fc2_setfam_1,fc2_subset_1,fc3_realset1,fc8_membered,rc1_finset_1,rc1_xboole_0,rc2_xboole_0,t1_subset,t6_boole,t7_boole,t8_boole,e1_1__amistd_1,d1_pre_circ]),
    [interesting(0.8),file(amistd_1,e2_1__amistd_1),[file(amistd_1,e2_1__amistd_1)]]).

fof(i2_1__amistd_1,theorem,(
    $true ),
    introduced(tautology,[file(amistd_1,i2_1__amistd_1)]),
    [interesting(0.8),trivial,file(amistd_1,i2_1__amistd_1)]).

fof(i1_1__amistd_1,plain,(
    k1_pre_circ(k1_tarski(c1_1__amistd_1)) = c1_1__amistd_1 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_1__amistd_1])],[e2_1__amistd_1,i2_1__amistd_1]),
    [interesting(0.8),file(amistd_1,i1_1__amistd_1),[file(amistd_1,i1_1__amistd_1)]]).

fof(i1_1_tmp__amistd_1,plain,
    ( v1_xreal_0(c1_1__amistd_1)
   => k1_pre_circ(k1_tarski(c1_1__amistd_1)) = c1_1__amistd_1 ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_1__amistd_1])],[dt_c1_1__amistd_1,i1_1__amistd_1]),
    [interesting(1),t1_amistd_1]).

fof(t1_amistd_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => k1_pre_circ(k1_tarski(A)) = A ) ),
    inference(let,[status(thm),assumptions([])],[i1_1_tmp__amistd_1,dh_c1_1__amistd_1]),
    [interesting(1),file(amistd_1,t1_amistd_1),[file(amistd_1,t1_amistd_1)]]).