% Mizar ND problem: t39_funct_6,funct_6,861,35 
fof(dh_c1_41__funct_6,definition,
    ( ( k3_card_3(k9_finseq_1(c1_41__funct_6)) = c1_41__funct_6
      & k4_funct_6(k9_finseq_1(c1_41__funct_6)) = c1_41__funct_6 )
   => ! [A] : 
        ( k3_card_3(k9_finseq_1(A)) = A
        & k4_funct_6(k9_finseq_1(A)) = A ) ),
    introduced(definition,[new_symbol(c1_41__funct_6),file(funct_6,c1_41__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_41__funct_6)]).

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_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_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(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(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(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

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(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(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(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(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(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(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(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(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(fc11_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k2_relat_1(A)) ) ),
    file(finseq_1,fc11_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc11_finseq_1)]).

fof(fc6_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k2_relat_1(A)) ) ),
    file(relat_1,fc6_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc6_relat_1)]).

fof(fc8_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k2_relat_1(A))
        & v1_relat_1(k2_relat_1(A)) ) ) ),
    file(relat_1,fc8_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc8_relat_1)]).

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_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(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_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(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(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(dt_k5_finseq_1,axiom,(
    $true ),
    file(finseq_1,k5_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k5_finseq_1)]).

fof(fc12_finseq_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(k5_finseq_1(A))
      & v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc12_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc12_finseq_1)]).

fof(fc3_finseq_1,theorem,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc3_finseq_1)]).

fof(fc4_finseq_1,theorem,(
    ! [A] : 
      ( v1_relat_1(k5_finseq_1(A))
      & v1_funct_1(k5_finseq_1(A))
      & v1_finset_1(k5_finseq_1(A))
      & v1_finseq_1(k5_finseq_1(A)) ) ),
    file(finseq_1,fc4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc4_finseq_1)]).

fof(redefinition_k9_finseq_1,definition,(
    ! [A] : k9_finseq_1(A) = k5_finseq_1(A) ),
    file(finseq_1,k9_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    [interesting(0.9),axiom,file(relat_1,k2_relat_1)]).

fof(dt_k3_card_3,axiom,(
    $true ),
    file(card_3,k3_card_3),
    [interesting(0.9),axiom,file(card_3,k3_card_3)]).

fof(dt_k3_tarski,axiom,(
    $true ),
    file(tarski,k3_tarski),
    [interesting(0.9),axiom,file(tarski,k3_tarski)]).

fof(dt_k9_finseq_1,axiom,(
    ! [A] : 
      ( v1_relat_1(k9_finseq_1(A))
      & v1_funct_1(k9_finseq_1(A)) ) ),
    file(finseq_1,k9_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k9_finseq_1)]).

fof(dt_c1_41__funct_6,assumption,(
    $true ),
    introduced(assumption,[file(funct_6,c1_41__funct_6)]),
    [interesting(0.8),axiom,file(funct_6,c1_41__funct_6)]).

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(d4_card_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k3_card_3(A) = k3_tarski(k2_relat_1(A)) ) ),
    file(card_3,d4_card_3),
    [interesting(0.9),axiom,file(card_3,d4_card_3)]).

fof(e1_41_1__funct_6,plain,(
    k3_card_3(k9_finseq_1(c1_41__funct_6)) = k3_tarski(k2_relat_1(k9_finseq_1(c1_41__funct_6))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_41__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,rc3_relat_1,rc4_funct_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,t1_subset,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc6_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc7_finseq_1,rc8_finseq_1,t6_boole,t7_boole,t8_boole,dt_k5_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,redefinition_k9_finseq_1,dt_k2_relat_1,dt_k3_card_3,dt_k3_tarski,dt_k9_finseq_1,dt_c1_41__funct_6,rc1_funct_1,d4_card_3]),
    [interesting(0.65),file(funct_6,e1_41_1__funct_6),[file(funct_6,e1_41_1__funct_6)]]).

fof(cc1_arytm_3,theorem,(
    ! [A] : 
      ( v3_ordinal1(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_ordinal1(B)
            & v2_ordinal1(B)
            & v3_ordinal1(B) ) ) ) ),
    file(arytm_3,cc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc1_arytm_3)]).

fof(cc2_arytm_3,theorem,(
    ! [A] : 
      ( ( v1_xboole_0(A)
        & v3_ordinal1(A) )
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc2_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc2_arytm_3)]).

fof(rc1_arytm_3,theorem,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A) ) ),
    file(arytm_3,rc1_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,rc1_arytm_3)]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    [interesting(0.9),axiom,file(ordinal2,k5_ordinal2)]).

fof(cc3_arytm_3,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_ordinal2)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A) ) ) ),
    file(arytm_3,cc3_arytm_3),
    [interesting(0.9),axiom,file(arytm_3,cc3_arytm_3)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(redefinition_k5_numbers,definition,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(redefinition_m2_subset_1,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(dt_k1_finseq_1,axiom,(
    $true ),
    file(finseq_1,k1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k1_finseq_1)]).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    [interesting(0.9),axiom,file(numbers,k1_numbers)]).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    [interesting(0.9),axiom,file(relat_1,k1_relat_1)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_k5_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    [interesting(0.9),axiom,file(numbers,k5_numbers)]).

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    [interesting(0.9),axiom,file(subset_1,m2_subset_1)]).

fof(fc17_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finset_1(A) )
     => v1_finset_1(k1_relat_1(A)) ) ),
    file(finseq_1,fc17_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc17_finseq_1)]).

fof(fc1_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => v1_finset_1(k1_finseq_1(A)) ) ),
    file(finseq_1,fc1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,fc1_finseq_1)]).

fof(fc1_subset_1,theorem,(
    ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) ),
    file(subset_1,fc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,fc1_subset_1)]).

fof(fc5_relat_1,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A) )
     => ~ v1_xboole_0(k1_relat_1(A)) ) ),
    file(relat_1,fc5_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc5_relat_1)]).

fof(fc7_relat_1,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_xboole_0(k1_relat_1(A))
        & v1_relat_1(k1_relat_1(A)) ) ) ),
    file(relat_1,fc7_relat_1),
    [interesting(0.9),axiom,file(relat_1,fc7_relat_1)]).

fof(rc1_subset_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
          & ~ v1_xboole_0(B) ) ) ),
    file(subset_1,rc1_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc1_subset_1)]).

fof(rc2_subset_1,theorem,(
    ! [A] : 
    ? [B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
      & v1_xboole_0(B) ) ),
    file(subset_1,rc2_subset_1),
    [interesting(0.9),axiom,file(subset_1,rc2_subset_1)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(redefinition_k2_finseq_1,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k2_finseq_1(A) = k1_finseq_1(A) ) ),
    file(finseq_1,k2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]).

fof(redefinition_k4_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k4_finseq_1(A) = k1_relat_1(A) ) ),
    file(finseq_1,k4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k4_finseq_1)]).

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

fof(dt_k2_finseq_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k2_finseq_1)]).

fof(dt_k4_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k5_numbers)) ) ),
    file(finseq_1,k4_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k4_finseq_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(spc1_numerals,theorem,
    ( v2_xreal_0(1)
    & m2_subset_1(1,k1_numbers,k5_numbers)
    & m1_subset_1(1,k5_numbers)
    & m1_subset_1(1,k1_numbers) ),
    file(numerals,spc1_numerals),
    [interesting(0.9),axiom,file(numerals,spc1_numerals)]).

fof(spc1_boole,theorem,(
    ~ v1_xboole_0(1) ),
    file(boole,spc1_boole),
    [interesting(0.9),axiom,file(boole,spc1_boole)]).

fof(t55_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k4_finseq_1(B) = k2_finseq_1(1)
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    file(finseq_1,t55_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t55_finseq_1)]).

fof(e2_41_1__funct_6,plain,(
    k3_tarski(k2_relat_1(k9_finseq_1(c1_41__funct_6))) = k3_tarski(k1_tarski(c1_41__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_41__funct_6])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc12_finseq_1,fc17_finseq_1,fc1_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,redefinition_k2_finseq_1,redefinition_k4_finseq_1,redefinition_k9_finseq_1,dt_k1_tarski,dt_k2_finseq_1,dt_k2_relat_1,dt_k3_tarski,dt_k4_finseq_1,dt_k9_finseq_1,dt_c1_41__funct_6,cc1_finseq_1,fc2_subset_1,rc1_finseq_1,rc1_funct_1,spc1_numerals,spc1_boole,t55_finseq_1]),
    [interesting(0.65),file(funct_6,e2_41_1__funct_6),[file(funct_6,e2_41_1__funct_6)]]).

fof(t31_zfmisc_1,theorem,(
    ! [A] : k3_tarski(k1_tarski(A)) = A ),
    file(zfmisc_1,t31_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,t31_zfmisc_1)]).

fof(e3_41_1__funct_6,plain,(
    k3_tarski(k1_tarski(c1_41__funct_6)) = c1_41__funct_6 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_41__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t1_subset,cc1_funct_1,cc1_relat_1,t6_boole,t7_boole,t8_boole,dt_k1_tarski,dt_k3_tarski,dt_c1_41__funct_6,fc2_subset_1,t31_zfmisc_1]),
    [interesting(0.65),file(funct_6,e3_41_1__funct_6),[file(funct_6,e3_41_1__funct_6)]]).

fof(e1_41__funct_6,plain,(
    k3_card_3(k9_finseq_1(c1_41__funct_6)) = c1_41__funct_6 ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_41__funct_6])],[e1_41_1__funct_6,e2_41_1__funct_6,e3_41_1__funct_6]),
    [interesting(0.8),file(funct_6,e1_41__funct_6),[file(funct_6,e1_41__funct_6)]]).

fof(dt_k1_setfam_1,axiom,(
    $true ),
    file(setfam_1,k1_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,k1_setfam_1)]).

fof(dt_k4_funct_6,axiom,(
    $true ),
    file(funct_6,k4_funct_6),
    [interesting(0.9),axiom,file(funct_6,k4_funct_6)]).

fof(d4_funct_6,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => k4_funct_6(A) = k1_setfam_1(k2_relat_1(A)) ) ),
    file(funct_6,d4_funct_6),
    [interesting(0.9),axiom,file(funct_6,d4_funct_6)]).

fof(e1_41_2__funct_6,plain,(
    k4_funct_6(k9_finseq_1(c1_41__funct_6)) = k1_setfam_1(k2_relat_1(k9_finseq_1(c1_41__funct_6))) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_41__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,rc3_relat_1,rc4_funct_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,t1_subset,cc1_finseq_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc6_relat_1,fc8_relat_1,rc1_finseq_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,rc7_finseq_1,rc8_finseq_1,t6_boole,t7_boole,t8_boole,dt_k5_finseq_1,fc12_finseq_1,fc3_finseq_1,fc4_finseq_1,rc1_funct_1,redefinition_k9_finseq_1,dt_k1_setfam_1,dt_k2_relat_1,dt_k4_funct_6,dt_k9_finseq_1,dt_c1_41__funct_6,d4_funct_6]),
    [interesting(0.65),file(funct_6,e1_41_2__funct_6),[file(funct_6,e1_41_2__funct_6)]]).

fof(e2_41_2__funct_6,plain,(
    k1_setfam_1(k2_relat_1(k9_finseq_1(c1_41__funct_6))) = k1_setfam_1(k1_tarski(c1_41__funct_6)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_41__funct_6])],[cc1_arytm_3,cc2_arytm_3,rc1_arytm_3,rc3_relat_1,rc4_funct_1,reflexivity_r1_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k5_ordinal2,cc3_arytm_3,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc3_finseq_1,rc3_funct_1,rc6_finseq_1,t1_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_relat_1,dt_k1_zfmisc_1,dt_k5_finseq_1,dt_k5_numbers,dt_m1_subset_1,dt_m2_subset_1,cc1_funct_1,cc1_relat_1,cc2_funct_1,fc11_finseq_1,fc12_finseq_1,fc17_finseq_1,fc1_finseq_1,fc1_subset_1,fc3_finseq_1,fc4_finseq_1,fc5_relat_1,fc6_relat_1,fc7_relat_1,fc8_relat_1,rc1_relat_1,rc1_subset_1,rc2_funct_1,rc2_relat_1,rc2_subset_1,rc7_finseq_1,rc8_finseq_1,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,redefinition_k2_finseq_1,redefinition_k4_finseq_1,redefinition_k9_finseq_1,dt_k1_setfam_1,dt_k1_tarski,dt_k2_finseq_1,dt_k2_relat_1,dt_k4_finseq_1,dt_k9_finseq_1,dt_c1_41__funct_6,cc1_finseq_1,fc2_subset_1,rc1_finseq_1,rc1_funct_1,spc1_numerals,spc1_boole,t55_finseq_1]),
    [interesting(0.65),file(funct_6,e2_41_2__funct_6),[file(funct_6,e2_41_2__funct_6)]]).

fof(t11_setfam_1,theorem,(
    ! [A] : k1_setfam_1(k1_tarski(A)) = A ),
    file(setfam_1,t11_setfam_1),
    [interesting(0.9),axiom,file(setfam_1,t11_setfam_1)]).

fof(e3_41_2__funct_6,plain,(
    k1_setfam_1(k1_tarski(c1_41__funct_6)) = c1_41__funct_6 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_41__funct_6])],[existence_m1_subset_1,dt_m1_subset_1,cc1_finseq_1,rc1_finseq_1,rc3_finseq_1,rc3_funct_1,rc3_relat_1,rc4_funct_1,rc6_finseq_1,rc7_finseq_1,rc8_finseq_1,t2_subset,antisymmetry_r2_hidden,dt_k1_xboole_0,cc2_funct_1,fc12_relat_1,fc2_finseq_1,fc4_relat_1,rc1_funct_1,rc1_relat_1,rc2_funct_1,rc2_relat_1,t1_subset,cc1_funct_1,cc1_relat_1,t6_boole,t7_boole,t8_boole,dt_k1_setfam_1,dt_k1_tarski,dt_c1_41__funct_6,fc2_subset_1,t11_setfam_1]),
    [interesting(0.65),file(funct_6,e3_41_2__funct_6),[file(funct_6,e3_41_2__funct_6)]]).

fof(e2_41__funct_6,plain,(
    k4_funct_6(k9_finseq_1(c1_41__funct_6)) = c1_41__funct_6 ),
    inference(iterative_eq,[status(thm),assumptions([dt_c1_41__funct_6])],[e1_41_2__funct_6,e2_41_2__funct_6,e3_41_2__funct_6]),
    [interesting(0.8),file(funct_6,e2_41__funct_6),[file(funct_6,e2_41__funct_6)]]).

fof(i3_41__funct_6,theorem,(
    $true ),
    introduced(tautology,[file(funct_6,i3_41__funct_6)]),
    [interesting(0.8),trivial,file(funct_6,i3_41__funct_6)]).

fof(i2_41__funct_6,plain,(
    k4_funct_6(k9_finseq_1(c1_41__funct_6)) = c1_41__funct_6 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_41__funct_6])],[e2_41__funct_6,i3_41__funct_6]),
    [interesting(0.8),file(funct_6,i2_41__funct_6),[file(funct_6,i2_41__funct_6)]]).

fof(i1_41__funct_6,plain,
    ( k3_card_3(k9_finseq_1(c1_41__funct_6)) = c1_41__funct_6
    & k4_funct_6(k9_finseq_1(c1_41__funct_6)) = c1_41__funct_6 ),
    inference(conclusion,[status(thm),assumptions([dt_c1_41__funct_6])],[e1_41__funct_6,i2_41__funct_6]),
    [interesting(0.8),file(funct_6,i1_41__funct_6),[file(funct_6,i1_41__funct_6)]]).

fof(i1_41_tmp__funct_6,plain,
    ( k3_card_3(k9_finseq_1(c1_41__funct_6)) = c1_41__funct_6
    & k4_funct_6(k9_finseq_1(c1_41__funct_6)) = c1_41__funct_6 ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_41__funct_6])],[dt_c1_41__funct_6,i1_41__funct_6]),
    [interesting(1),t39_funct_6]).

fof(t39_funct_6,theorem,(
    ! [A] : 
      ( k3_card_3(k9_finseq_1(A)) = A
      & k4_funct_6(k9_finseq_1(A)) = A ) ),
    inference(let,[status(thm),assumptions([])],[i1_41_tmp__funct_6,dh_c1_41__funct_6]),
    [interesting(1),file(funct_6,t39_funct_6),[file(funct_6,t39_funct_6)]]).