% Mizar ND problem: t6_binari_3,binari_3,172,19 
fof(dh_c1_6__binari_3,definition,
    ( ( m2_subset_1(c1_6__binari_3,k1_numbers,k5_numbers)
     => ! [A] : 
          ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(c1_6__binari_3,k6_margrel1))
         => ( A = k5_euclid(c1_6__binari_3)
           => k6_binarith(c1_6__binari_3,A) = k4_finseqop(k1_numbers,c1_6__binari_3,1) ) ) )
   => ! [B] : 
        ( m2_subset_1(B,k1_numbers,k5_numbers)
       => ! [C] : 
            ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(B,k6_margrel1))
           => ( C = k5_euclid(B)
             => k6_binarith(B,C) = k4_finseqop(k1_numbers,B,1) ) ) ) ),
    introduced(definition,[new_symbol(c1_6__binari_3),file(binari_3,c1_6__binari_3)]),
    [interesting(0.8),axiom,file(binari_3,c1_6__binari_3)]).

fof(dh_c2_6__binari_3,definition,
    ( ( m2_finseq_2(c2_6__binari_3,k6_margrel1,k4_finseq_2(c1_6__binari_3,k6_margrel1))
     => ( c2_6__binari_3 = k5_euclid(c1_6__binari_3)
       => k6_binarith(c1_6__binari_3,c2_6__binari_3) = k4_finseqop(k1_numbers,c1_6__binari_3,1) ) )
   => ! [A] : 
        ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(c1_6__binari_3,k6_margrel1))
       => ( A = k5_euclid(c1_6__binari_3)
         => k6_binarith(c1_6__binari_3,A) = k4_finseqop(k1_numbers,c1_6__binari_3,1) ) ) ),
    introduced(definition,[new_symbol(c2_6__binari_3),file(binari_3,c2_6__binari_3)]),
    [interesting(0.8),axiom,file(binari_3,c2_6__binari_3)]).

fof(e1_6__binari_3,assumption,(
    c2_6__binari_3 = k5_euclid(c1_6__binari_3) ),
    introduced(assumption,[file(binari_3,e1_6__binari_3)]),
    [interesting(0.8),axiom,file(binari_3,e1_6__binari_3)]).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k2_zfmisc_1)]).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    [interesting(0.9),axiom,file(relset_1,m1_relset_1)]).

fof(cc1_relset_1,theorem,(
    ! [A,B,C] : 
      ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
     => v1_relat_1(C) ) ),
    file(relset_1,cc1_relset_1),
    [interesting(0.9),axiom,file(relset_1,cc1_relset_1)]).

fof(existence_m1_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_1(B,A) ),
    file(finseq_1,m1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]).

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(redefinition_m2_relset_1,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(dt_m1_finseq_1,axiom,(
    ! [A,B] : 
      ( m1_finseq_1(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) ) ) ),
    file(finseq_1,m1_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m1_finseq_1)]).

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    [interesting(0.9),axiom,file(relset_1,m2_relset_1)]).

fof(fc14_membered,theorem,(
    ! [A,B] : 
      ( ( v1_rat_1(A)
        & v1_rat_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc14_membered),
    [interesting(0.9),axiom,file(membered,fc14_membered)]).

fof(fc15_membered,theorem,(
    ! [A,B] : 
      ( ( v1_int_1(A)
        & v1_int_1(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc15_membered),
    [interesting(0.9),axiom,file(membered,fc15_membered)]).

fof(rc1_margrel1,theorem,(
    ? [A] : v1_margrel1(A) ),
    file(margrel1,rc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc1_margrel1)]).

fof(commutativity_k2_tarski,theorem,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

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

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(existence_m1_finseq_2,axiom,(
    ! [A] : 
    ? [B] : m1_finseq_2(B,A) ),
    file(finseq_2,m1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]).

fof(existence_m2_finseq_1,axiom,(
    ! [A] : 
    ? [B] : m2_finseq_1(B,A) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]).

fof(redefinition_m2_finseq_1,definition,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
    <=> m1_finseq_1(B,A) ) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_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_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    [interesting(0.9),axiom,file(tarski,k2_tarski)]).

fof(dt_m1_finseq_2,axiom,(
    $true ),
    file(finseq_2,m1_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m1_finseq_2)]).

fof(dt_m2_finseq_1,axiom,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ( v1_funct_1(B)
        & v1_finseq_1(B)
        & m2_relset_1(B,k5_numbers,A) ) ) ),
    file(finseq_1,m2_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,m2_finseq_1)]).

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(cc18_membered,theorem,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    [interesting(0.9),axiom,file(membered,cc18_membered)]).

fof(cc19_membered,theorem,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    [interesting(0.9),axiom,file(membered,cc19_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(cc20_membered,theorem,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    [interesting(0.9),axiom,file(membered,cc20_membered)]).

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(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(fc12_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_membered(k2_tarski(A,B)) ) ),
    file(membered,fc12_membered),
    [interesting(0.9),axiom,file(membered,fc12_membered)]).

fof(fc13_membered,theorem,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc13_membered),
    [interesting(0.9),axiom,file(membered,fc13_membered)]).

fof(fc16_membered,theorem,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v1_membered(k2_tarski(A,B))
        & v2_membered(k2_tarski(A,B))
        & v3_membered(k2_tarski(A,B))
        & v4_membered(k2_tarski(A,B))
        & v5_membered(k2_tarski(A,B)) ) ) ),
    file(membered,fc16_membered),
    [interesting(0.9),axiom,file(membered,fc16_membered)]).

fof(fc1_margrel1,theorem,
    ( v1_xboole_0(k1_xboole_0)
    & v1_margrel1(k1_xboole_0) ),
    file(margrel1,fc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc1_margrel1)]).

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_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_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(rc2_margrel1,theorem,(
    ? [A] : v2_margrel1(A) ),
    file(margrel1,rc2_margrel1),
    [interesting(0.9),axiom,file(margrel1,rc2_margrel1)]).

fof(rc2_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc2_nat_1)]).

fof(rc3_nat_1,theorem,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    [interesting(0.9),axiom,file(nat_1,rc3_nat_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(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(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_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    [interesting(0.9),axiom,file(real,t5_real)]).

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(t6_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    [interesting(0.9),axiom,file(real,t6_real)]).

fof(t7_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    [interesting(0.9),axiom,file(real,t7_real)]).

fof(t8_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    [interesting(0.9),axiom,file(real,t8_real)]).

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(existence_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ? [C] : m2_finseq_2(C,A,B) ) ),
    file(finseq_2,m2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]).

fof(redefinition_m2_finseq_2,definition,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(finseq_2,m2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]).

fof(dt_k1_card_1,axiom,(
    ! [A] : v1_card_1(k1_card_1(A)) ),
    file(card_1,k1_card_1),
    [interesting(0.9),axiom,file(card_1,k1_card_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_k2_finseq_2,axiom,(
    ! [A,B] : 
      ( v4_ordinal2(A)
     => ( v1_relat_1(k2_finseq_2(A,B))
        & v1_funct_1(k2_finseq_2(A,B))
        & v1_finseq_1(k2_finseq_2(A,B)) ) ) ),
    file(finseq_2,k2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,k2_finseq_2)]).

fof(dt_k4_finseq_2,axiom,(
    ! [A,B] : 
      ( v4_ordinal2(A)
     => m1_finseq_2(k4_finseq_2(A,B),B) ) ),
    file(finseq_2,k4_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,k4_finseq_2)]).

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

fof(dt_k6_margrel1,axiom,(
    $true ),
    file(margrel1,k6_margrel1),
    [interesting(0.9),axiom,file(margrel1,k6_margrel1)]).

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

fof(dt_m2_finseq_2,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(B)
        & m1_finseq_2(B,A) )
     => ! [C] : 
          ( m2_finseq_2(C,A,B)
         => m2_finseq_1(C,A) ) ) ),
    file(finseq_2,m2_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,m2_finseq_2)]).

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(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(cc16_membered,theorem,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    [interesting(0.9),axiom,file(membered,cc16_membered)]).

fof(cc17_membered,theorem,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    [interesting(0.9),axiom,file(membered,cc17_membered)]).

fof(cc1_margrel1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => v2_margrel1(A) ) ),
    file(margrel1,cc1_margrel1),
    [interesting(0.9),axiom,file(margrel1,cc1_margrel1)]).

fof(cc1_nat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc1_nat_1)]).

fof(cc2_nat_1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    [interesting(0.9),axiom,file(nat_1,cc2_nat_1)]).

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

fof(cc6_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
     => ( v1_membered(A)
        & v2_membered(A) ) ) ),
    file(membered,cc6_membered),
    [interesting(0.9),axiom,file(membered,cc6_membered)]).

fof(cc9_membered,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k5_numbers))
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc9_membered),
    [interesting(0.9),axiom,file(membered,cc9_membered)]).

fof(fc3_margrel1,theorem,(
    ~ v1_xboole_0(k6_margrel1) ),
    file(margrel1,fc3_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc3_margrel1)]).

fof(fc5_membered,theorem,
    ( v1_membered(k5_ordinal2)
    & v2_membered(k5_ordinal2)
    & v3_membered(k5_ordinal2)
    & v4_membered(k5_ordinal2)
    & v5_membered(k5_ordinal2) ),
    file(membered,fc5_membered),
    [interesting(0.9),axiom,file(membered,fc5_membered)]).

fof(t1_numerals,theorem,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    [interesting(0.9),axiom,file(numerals,t1_numerals)]).

fof(t1_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    [interesting(0.9),axiom,file(real,t1_real)]).

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(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(t4_real,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    [interesting(0.9),axiom,file(real,t4_real)]).

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(d12_margrel1,definition,(
    k6_margrel1 = k2_tarski(0,1) ),
    file(margrel1,d12_margrel1),
    [interesting(0.9),axiom,file(margrel1,d12_margrel1)]).

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(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_k3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_1(A) = k1_card_1(A) ) ),
    file(finseq_1,k3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]).

fof(redefinition_k4_finseqop,definition,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,A) )
     => k4_finseqop(A,B,C) = k2_finseq_2(B,C) ) ),
    file(finseqop,k4_finseqop),
    [interesting(0.9),axiom,file(finseqop,k4_finseqop)]).

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_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    [interesting(0.9),axiom,file(funct_1,k1_funct_1)]).

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

fof(dt_k3_finseq_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => m2_subset_1(k3_finseq_1(A),k1_numbers,k5_numbers) ) ),
    file(finseq_1,k3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,k3_finseq_1)]).

fof(dt_k4_finseqop,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & m1_subset_1(B,k5_numbers)
        & m1_subset_1(C,A) )
     => m2_finseq_2(k4_finseqop(A,B,C),A,k4_finseq_2(B,A)) ) ),
    file(finseqop,k4_finseqop),
    [interesting(0.9),axiom,file(finseqop,k4_finseqop)]).

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_k6_binarith,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k4_finseq_2(A,k6_margrel1)) )
     => m2_finseq_2(k6_binarith(A,B),k6_margrel1,k4_finseq_2(A,k6_margrel1)) ) ),
    file(binarith,k6_binarith),
    [interesting(0.9),axiom,file(binarith,k6_binarith)]).

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(dt_c1_6__binari_3,assumption,(
    m2_subset_1(c1_6__binari_3,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(binari_3,c1_6__binari_3)]),
    [interesting(0.8),axiom,file(binari_3,c1_6__binari_3)]).

fof(dt_c2_6__binari_3,assumption,(
    m2_finseq_2(c2_6__binari_3,k6_margrel1,k4_finseq_2(c1_6__binari_3,k6_margrel1)) ),
    introduced(assumption,[file(binari_3,c2_6__binari_3)]),
    [interesting(0.8),axiom,file(binari_3,c2_6__binari_3)]).

fof(fc2_membered,theorem,
    ( ~ v1_xboole_0(k1_numbers)
    & v1_membered(k1_numbers)
    & v2_membered(k1_numbers) ),
    file(membered,fc2_membered),
    [interesting(0.9),axiom,file(membered,fc2_membered)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r0,theorem,(
    ~ r1_xreal_0(1,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r0)]).

fof(spc0_numerals,theorem,
    ( v2_xreal_0(0)
    & m2_subset_1(0,k1_numbers,k5_numbers)
    & m1_subset_1(0,k5_numbers)
    & m1_subset_1(0,k1_numbers) ),
    file(numerals,spc0_numerals),
    [interesting(0.9),axiom,file(numerals,spc0_numerals)]).

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(spc0_boole,theorem,(
    v1_xboole_0(0) ),
    file(boole,spc0_boole),
    [interesting(0.9),axiom,file(boole,spc0_boole)]).

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

fof(dh_c1_6_2__binari_3,definition,
    ( ( m2_subset_1(c1_6_2__binari_3,k1_numbers,k5_numbers)
     => ( ( r1_xreal_0(1,c1_6_2__binari_3)
          & r1_xreal_0(c1_6_2__binari_3,k3_finseq_1(k6_binarith(c1_6__binari_3,c2_6__binari_3))) )
       => k1_funct_1(k6_binarith(c1_6__binari_3,c2_6__binari_3),c1_6_2__binari_3) = k1_funct_1(k4_finseqop(k1_numbers,c1_6__binari_3,1),c1_6_2__binari_3) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => ( ( r1_xreal_0(1,A)
            & r1_xreal_0(A,k3_finseq_1(k6_binarith(c1_6__binari_3,c2_6__binari_3))) )
         => k1_funct_1(k6_binarith(c1_6__binari_3,c2_6__binari_3),A) = k1_funct_1(k4_finseqop(k1_numbers,c1_6__binari_3,1),A) ) ) ),
    introduced(definition,[new_symbol(c1_6_2__binari_3),file(binari_3,c1_6_2__binari_3)]),
    [interesting(0.65),axiom,file(binari_3,c1_6_2__binari_3)]).

fof(e1_6_2__binari_3,assumption,(
    r1_xreal_0(1,c1_6_2__binari_3) ),
    introduced(assumption,[file(binari_3,e1_6_2__binari_3)]),
    [interesting(0.65),axiom,file(binari_3,e1_6_2__binari_3)]).

fof(e2_6_2__binari_3,assumption,(
    r1_xreal_0(c1_6_2__binari_3,k3_finseq_1(k6_binarith(c1_6__binari_3,c2_6__binari_3))) ),
    introduced(assumption,[file(binari_3,e2_6_2__binari_3)]),
    [interesting(0.65),axiom,file(binari_3,e2_6_2__binari_3)]).

fof(dt_k4_finseq_4,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(C)
        & m1_relset_1(C,A,B) )
     => m1_subset_1(k4_finseq_4(A,B,C,D),B) ) ),
    file(finseq_4,k4_finseq_4),
    [interesting(0.9),axiom,file(finseq_4,k4_finseq_4)]).

fof(dt_c1_6_2__binari_3,assumption,(
    m2_subset_1(c1_6_2__binari_3,k1_numbers,k5_numbers) ),
    introduced(assumption,[file(binari_3,c1_6_2__binari_3)]),
    [interesting(0.65),axiom,file(binari_3,c1_6_2__binari_3)]).

fof(t24_finseq_4,theorem,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ! [C] : 
          ( m2_subset_1(C,k1_numbers,k5_numbers)
         => ( ( r1_xreal_0(1,C)
              & r1_xreal_0(C,k3_finseq_1(B)) )
           => k4_finseq_4(k5_numbers,A,B,C) = k1_funct_1(B,C) ) ) ) ),
    file(finseq_4,t24_finseq_4),
    [interesting(0.9),axiom,file(finseq_4,t24_finseq_4)]).

fof(rqLessOrEqual__r1_xreal_0__r1_r1,theorem,(
    r1_xreal_0(1,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r1_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r1,theorem,(
    r1_xreal_0(0,1) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r1)]).

fof(rqLessOrEqual__r1_xreal_0__r0_r0,theorem,(
    r1_xreal_0(0,0) ),
    file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0),
    [interesting(0.9),axiom,file(arithm,rqLessOrEqual__r1_xreal_0__r0_r0)]).

fof(e1_6_2_2__binari_3,plain,(
    k1_funct_1(k6_binarith(c1_6__binari_3,c2_6__binari_3),c1_6_2__binari_3) = k4_finseq_4(k5_numbers,k6_margrel1,k6_binarith(c1_6__binari_3,c2_6__binari_3),c1_6_2__binari_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__binari_3,dt_c1_6_2__binari_3,dt_c2_6__binari_3,e1_6_2__binari_3,e2_6_2__binari_3])],[fc14_membered,fc15_membered,rc1_margrel1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_2,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_finseq_2,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,fc12_membered,fc16_membered,fc1_margrel1,fc6_membered,rc1_membered,rc1_nat_1,rc2_margrel1,rc2_nat_1,rc3_nat_1,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k2_tarski,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_ordinal2,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_margrel1,cc1_nat_1,cc2_nat_1,cc4_membered,cc6_membered,cc9_membered,fc13_membered,fc5_membered,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_4,dt_k5_numbers,dt_k6_binarith,dt_k6_margrel1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_6__binari_3,dt_c1_6_2__binari_3,dt_c2_6__binari_3,fc2_membered,fc3_margrel1,rqLessOrEqual__r1_xreal_0__r1_r0,d12_margrel1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_6_2__binari_3,e2_6_2__binari_3,t24_finseq_4,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.5),file(binari_3,e1_6_2_2__binari_3),[file(binari_3,e1_6_2_2__binari_3)]]).

fof(fc4_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,fc4_margrel1),
    [interesting(0.9),axiom,file(margrel1,fc4_margrel1)]).

fof(involutiveness_k9_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,k9_margrel1),
    [interesting(0.9),axiom,file(margrel1,k9_margrel1)]).

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_k9_margrel1,axiom,(
    ! [A] : 
      ( v2_margrel1(A)
     => v2_margrel1(k9_margrel1(A)) ) ),
    file(margrel1,k9_margrel1),
    [interesting(0.9),axiom,file(margrel1,k9_margrel1)]).

fof(involutiveness_k11_margrel1,theorem,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => k11_margrel1(k11_margrel1(A)) = A ) ),
    file(margrel1,k11_margrel1),
    [interesting(0.9),axiom,file(margrel1,k11_margrel1)]).

fof(redefinition_k11_margrel1,definition,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => k11_margrel1(A) = k9_margrel1(A) ) ),
    file(margrel1,k11_margrel1),
    [interesting(0.9),axiom,file(margrel1,k11_margrel1)]).

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(dt_k11_margrel1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k6_margrel1)
     => m1_subset_1(k11_margrel1(A),k6_margrel1) ) ),
    file(margrel1,k11_margrel1),
    [interesting(0.9),axiom,file(margrel1,k11_margrel1)]).

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(t109_finseq_2,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_2(C,B,k4_finseq_2(A,B))
             => k3_finseq_1(C) = A ) ) ) ),
    file(finseq_2,t109_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,t109_finseq_2)]).

fof(e3_6_2__binari_3,plain,
    ( k3_finseq_1(k6_binarith(c1_6__binari_3,c2_6__binari_3)) = c1_6__binari_3
    & k3_finseq_1(c2_6__binari_3) = c1_6__binari_3 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__binari_3,dt_c2_6__binari_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,commutativity_k2_tarski,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k2_tarski,dt_m1_finseq_1,dt_m2_relset_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_margrel1,rc1_nat_1,rc2_margrel1,rc2_nat_1,rc3_nat_1,spc0_boole,spc1_boole,t1_numerals,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k6_margrel1,dt_m1_finseq_2,dt_m1_subset_1,dt_m2_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_margrel1,cc1_membered,cc1_nat_1,cc20_membered,cc2_membered,cc2_nat_1,cc3_membered,cc3_nat_1,cc4_membered,cc6_membered,cc9_membered,fc1_margrel1,fc3_margrel1,fc5_membered,fc6_membered,rc1_membered,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,d12_margrel1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_2,dt_k5_numbers,dt_k6_binarith,dt_m2_finseq_2,dt_m2_subset_1,dt_c1_6__binari_3,dt_c2_6__binari_3,cc15_membered,fc2_membered,t6_boole,t7_boole,t8_boole,t109_finseq_2]),
    [interesting(0.65),file(binari_3,e3_6_2__binari_3),[file(binari_3,e3_6_2__binari_3)]]).

fof(t3_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(A,k2_finseq_1(B))
          <=> ( r1_xreal_0(1,A)
              & r1_xreal_0(A,B) ) ) ) ) ),
    file(finseq_1,t3_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t3_finseq_1)]).

fof(e4_6_2__binari_3,plain,(
    r2_hidden(c1_6_2__binari_3,k2_finseq_1(c1_6__binari_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2__binari_3,dt_c1_6__binari_3,dt_c2_6__binari_3,e1_6_2__binari_3,e2_6_2__binari_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,fc14_membered,fc15_membered,rc1_margrel1,commutativity_k2_tarski,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k2_tarski,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,fc12_membered,fc13_membered,fc16_membered,fc1_margrel1,fc5_membered,fc6_membered,rc1_membered,rc2_margrel1,rc2_nat_1,rc3_nat_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k1_finseq_1,dt_k1_numbers,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_numbers,dt_k6_margrel1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc15_membered,cc1_margrel1,cc1_nat_1,cc2_nat_1,cc6_membered,cc9_membered,fc2_membered,fc3_margrel1,rc1_nat_1,t1_numerals,t1_real,t2_real,t2_subset,t3_real,t3_subset,t4_real,t4_subset,t5_real,t5_subset,t6_boole,t6_real,t7_real,t8_boole,t8_real,d12_margrel1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,antisymmetry_r2_hidden,redefinition_k2_finseq_1,redefinition_k3_finseq_1,dt_k2_finseq_1,dt_k3_finseq_1,dt_k6_binarith,dt_c1_6__binari_3,dt_c1_6_2__binari_3,dt_c2_6__binari_3,cc3_nat_1,rqLessOrEqual__r1_xreal_0__r1_r0,t1_subset,t7_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_6_2__binari_3,e1_6_2__binari_3,e2_6_2__binari_3,t3_finseq_1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.65),file(binari_3,e4_6_2__binari_3),[file(binari_3,e4_6_2__binari_3)]]).

fof(d4_binarith,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ! [C] : 
              ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
             => ( C = k6_binarith(A,B)
              <=> ! [D] : 
                    ( m2_subset_1(D,k1_numbers,k5_numbers)
                   => ( r2_hidden(D,k2_finseq_1(A))
                     => k4_finseq_4(k5_numbers,k6_margrel1,C,D) = k11_margrel1(k4_finseq_4(k5_numbers,k6_margrel1,B,D)) ) ) ) ) ) ) ),
    file(binarith,d4_binarith),
    [interesting(0.9),axiom,file(binarith,d4_binarith)]).

fof(e2_6_2_2__binari_3,plain,(
    k4_finseq_4(k5_numbers,k6_margrel1,k6_binarith(c1_6__binari_3,c2_6__binari_3),c1_6_2__binari_3) = k11_margrel1(k4_finseq_4(k5_numbers,k6_margrel1,c2_6__binari_3,c1_6_2__binari_3)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2__binari_3,dt_c1_6__binari_3,dt_c2_6__binari_3,e1_6_2__binari_3,e2_6_2__binari_3])],[dt_k2_zfmisc_1,cc1_relset_1,fc14_membered,fc15_membered,rc1_margrel1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_m1_finseq_1,dt_m2_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,fc12_membered,fc13_membered,fc1_margrel1,fc4_margrel1,fc6_membered,rc1_membered,rc1_nat_1,rc2_margrel1,rc2_nat_1,rc3_nat_1,commutativity_k2_tarski,involutiveness_k9_margrel1,existence_m1_finseq_2,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_ordinal2,dt_k9_margrel1,dt_m1_finseq_2,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_margrel1,cc1_nat_1,cc2_nat_1,cc3_nat_1,cc4_membered,cc6_membered,cc9_membered,fc16_membered,fc5_membered,spc0_boole,spc1_boole,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,involutiveness_k11_margrel1,antisymmetry_r2_hidden,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k11_margrel1,redefinition_k2_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k11_margrel1,dt_k1_numbers,dt_k2_finseq_1,dt_k4_finseq_2,dt_k4_finseq_4,dt_k5_numbers,dt_k6_binarith,dt_k6_margrel1,dt_m2_finseq_2,dt_m2_subset_1,dt_c1_6__binari_3,dt_c1_6_2__binari_3,dt_c2_6__binari_3,fc2_membered,fc3_margrel1,t1_subset,t7_boole,d12_margrel1,e4_6_2__binari_3,d4_binarith]),
    [interesting(0.5),file(binari_3,e2_6_2_2__binari_3),[file(binari_3,e2_6_2_2__binari_3)]]).

fof(dt_k7_margrel1,axiom,(
    m1_subset_1(k7_margrel1,k6_margrel1) ),
    file(margrel1,k7_margrel1),
    [interesting(0.9),axiom,file(margrel1,k7_margrel1)]).

fof(d13_margrel1,definition,(
    k7_margrel1 = 0 ),
    file(margrel1,d13_margrel1),
    [interesting(0.9),axiom,file(margrel1,d13_margrel1)]).

fof(dt_k1_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( ~ v1_xboole_0(k1_euclid(A))
        & m1_finseq_2(k1_euclid(A),k1_numbers) ) ) ),
    file(euclid,k1_euclid),
    [interesting(0.9),axiom,file(euclid,k1_euclid)]).

fof(redefinition_k5_euclid,definition,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => k5_euclid(A) = k4_euclid(A) ) ),
    file(euclid,k5_euclid),
    [interesting(0.9),axiom,file(euclid,k5_euclid)]).

fof(dt_k4_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m2_finseq_1(k4_euclid(A),k1_numbers) ) ),
    file(euclid,k4_euclid),
    [interesting(0.9),axiom,file(euclid,k4_euclid)]).

fof(dt_k5_euclid,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => m2_finseq_2(k5_euclid(A),k1_numbers,k1_euclid(A)) ) ),
    file(euclid,k5_euclid),
    [interesting(0.9),axiom,file(euclid,k5_euclid)]).

fof(d4_euclid,definition,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => k4_euclid(A) = k4_finseqop(k1_numbers,A,0) ) ),
    file(euclid,d4_euclid),
    [interesting(0.9),axiom,file(euclid,d4_euclid)]).

fof(e1_6_2_1__binari_3,plain,(
    k1_funct_1(c2_6__binari_3,c1_6_2__binari_3) = k1_funct_1(k4_finseqop(k1_numbers,c1_6__binari_3,0),c1_6_2__binari_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__binari_3,dt_c1_6_2__binari_3,dt_c2_6__binari_3,e1_6__binari_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,fc14_membered,fc15_membered,rc1_margrel1,commutativity_k2_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_1,existence_m1_finseq_2,existence_m2_relset_1,redefinition_m2_relset_1,dt_k1_xboole_0,dt_k2_tarski,dt_m1_finseq_1,dt_m1_finseq_2,dt_m2_relset_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,fc12_membered,fc13_membered,fc16_membered,fc1_margrel1,fc6_membered,rc1_membered,rc1_nat_1,rc2_margrel1,rc2_nat_1,rc3_nat_1,spc1_boole,spc1_numerals,t1_subset,t4_subset,t5_subset,spc1_numerals,spc1_boole,existence_m1_subset_1,existence_m2_finseq_1,existence_m2_finseq_2,redefinition_m2_finseq_1,redefinition_m2_finseq_2,dt_k1_euclid,dt_k1_zfmisc_1,dt_k2_finseq_2,dt_k4_finseq_2,dt_k5_ordinal2,dt_k6_margrel1,dt_m1_subset_1,dt_m2_finseq_1,dt_m2_finseq_2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_margrel1,cc1_nat_1,cc2_nat_1,cc4_membered,cc6_membered,cc9_membered,fc3_margrel1,fc5_membered,t1_numerals,t2_subset,t3_subset,t6_boole,t7_boole,t8_boole,d12_margrel1,existence_m2_subset_1,redefinition_k4_finseqop,redefinition_k5_euclid,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k4_euclid,dt_k4_finseqop,dt_k5_euclid,dt_k5_numbers,dt_m2_subset_1,dt_c1_6__binari_3,dt_c1_6_2__binari_3,dt_c2_6__binari_3,fc2_membered,spc0_numerals,spc0_boole,e1_6__binari_3,d4_euclid]),
    [interesting(0.5),file(binari_3,e1_6_2_1__binari_3),[file(binari_3,e1_6_2_1__binari_3)]]).

fof(dt_k8_margrel1,axiom,(
    m1_subset_1(k8_margrel1,k6_margrel1) ),
    file(margrel1,k8_margrel1),
    [interesting(0.9),axiom,file(margrel1,k8_margrel1)]).

fof(d14_margrel1,definition,(
    k8_margrel1 = 1 ),
    file(margrel1,d14_margrel1),
    [interesting(0.9),axiom,file(margrel1,d14_margrel1)]).

fof(t70_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B,C] : 
          ( r2_hidden(B,k2_finseq_1(A))
         => k1_funct_1(k2_finseq_2(A,C),B) = C ) ) ),
    file(finseq_2,t70_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,t70_finseq_2)]).

fof(t36_margrel1,theorem,
    ( k7_margrel1 = 0
    & k8_margrel1 = 1 ),
    file(margrel1,t36_margrel1),
    [interesting(0.9),axiom,file(margrel1,t36_margrel1)]).

fof(e2_6_2_1__binari_3,plain,(
    k1_funct_1(k4_finseqop(k1_numbers,c1_6__binari_3,0),c1_6_2__binari_3) = k7_margrel1 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2__binari_3,dt_c1_6__binari_3,dt_c2_6__binari_3,e1_6_2__binari_3,e2_6_2__binari_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,fc14_membered,fc15_membered,rc1_margrel1,commutativity_k2_tarski,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k2_tarski,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,fc12_membered,fc13_membered,fc16_membered,fc1_margrel1,fc5_membered,fc6_membered,rc1_membered,rc2_margrel1,rc2_nat_1,rc3_nat_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_numbers,dt_k6_margrel1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_margrel1,cc1_nat_1,cc2_nat_1,cc4_membered,cc6_membered,cc9_membered,fc3_margrel1,rc1_nat_1,t1_numerals,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,d12_margrel1,antisymmetry_r2_hidden,redefinition_k2_finseq_1,redefinition_k4_finseqop,dt_k1_funct_1,dt_k1_numbers,dt_k2_finseq_1,dt_k2_finseq_2,dt_k4_finseqop,dt_k7_margrel1,dt_k8_margrel1,dt_c1_6__binari_3,dt_c1_6_2__binari_3,cc3_nat_1,fc2_membered,t1_subset,t7_boole,d13_margrel1,d14_margrel1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e4_6_2__binari_3,t70_finseq_2,t36_margrel1]),
    [interesting(0.5),file(binari_3,e2_6_2_1__binari_3),[file(binari_3,e2_6_2_1__binari_3)]]).

fof(e5_6_2__binari_3,plain,(
    k1_funct_1(c2_6__binari_3,c1_6_2__binari_3) = k7_margrel1 ),
    inference(iterative_eq,[status(thm),assumptions([e1_6__binari_3,dt_c1_6_2__binari_3,dt_c1_6__binari_3,dt_c2_6__binari_3,e1_6_2__binari_3,e2_6_2__binari_3])],[e1_6_2_1__binari_3,e2_6_2_1__binari_3]),
    [interesting(0.65),file(binari_3,e5_6_2__binari_3),[file(binari_3,e5_6_2__binari_3)]]).

fof(e3_6_2_2__binari_3,plain,(
    k11_margrel1(k4_finseq_4(k5_numbers,k6_margrel1,c2_6__binari_3,c1_6_2__binari_3)) = k11_margrel1(k7_margrel1) ),
    inference(mizar_by,[status(thm),assumptions([e1_6__binari_3,dt_c1_6_2__binari_3,dt_c1_6__binari_3,dt_c2_6__binari_3,e1_6_2__binari_3,e2_6_2__binari_3])],[fc14_membered,fc15_membered,rc1_margrel1,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_2,dt_k1_xboole_0,dt_k2_zfmisc_1,dt_m1_finseq_2,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc1_relset_1,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,fc12_membered,fc16_membered,fc1_margrel1,fc4_margrel1,fc6_membered,rc1_membered,rc1_nat_1,rc2_margrel1,rc2_nat_1,rc3_nat_1,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,commutativity_k2_tarski,involutiveness_k9_margrel1,existence_m1_finseq_1,existence_m1_relset_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_relset_1,redefinition_m2_finseq_2,redefinition_m2_relset_1,dt_k1_card_1,dt_k1_zfmisc_1,dt_k2_tarski,dt_k4_finseq_2,dt_k5_ordinal2,dt_k9_margrel1,dt_m1_finseq_1,dt_m1_relset_1,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_relset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_margrel1,cc1_nat_1,cc2_nat_1,cc4_membered,cc6_membered,cc9_membered,fc13_membered,fc5_membered,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,involutiveness_k11_margrel1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_finseq_1,existence_m2_subset_1,redefinition_k11_margrel1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_1,redefinition_m2_subset_1,dt_k11_margrel1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_4,dt_k5_numbers,dt_k6_binarith,dt_k6_margrel1,dt_k7_margrel1,dt_m2_finseq_1,dt_m2_subset_1,dt_c1_6__binari_3,dt_c1_6_2__binari_3,dt_c2_6__binari_3,fc2_membered,fc3_margrel1,rqLessOrEqual__r1_xreal_0__r1_r0,d12_margrel1,d13_margrel1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e1_6_2__binari_3,e2_6_2__binari_3,e3_6_2__binari_3,e5_6_2__binari_3,t24_finseq_4,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.5),file(binari_3,e3_6_2_2__binari_3),[file(binari_3,e3_6_2_2__binari_3)]]).

fof(t41_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( ( A = k7_margrel1
         => k9_margrel1(A) = k8_margrel1 )
        & ( k9_margrel1(A) = k8_margrel1
         => A = k7_margrel1 )
        & ( A = k8_margrel1
         => k9_margrel1(A) = k7_margrel1 )
        & ( k9_margrel1(A) = k7_margrel1
         => A = k8_margrel1 ) ) ) ),
    file(margrel1,t41_margrel1),
    [interesting(0.9),axiom,file(margrel1,t41_margrel1)]).

fof(e4_6_2_2__binari_3,plain,(
    k11_margrel1(k7_margrel1) = 1 ),
    inference(mizar_by,[status(thm),assumptions([])],[reflexivity_r1_tarski,fc14_membered,fc15_membered,rc1_margrel1,commutativity_k2_tarski,antisymmetry_r2_hidden,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k2_tarski,dt_k5_ordinal2,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,cc4_membered,cc6_membered,cc9_membered,fc12_membered,fc13_membered,fc16_membered,fc1_margrel1,fc5_membered,fc6_membered,rc1_membered,rc1_nat_1,rc2_nat_1,rc3_nat_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_numbers,dt_k5_numbers,dt_k6_margrel1,dt_m1_subset_1,dt_m2_subset_1,cc15_membered,cc1_margrel1,cc1_nat_1,cc2_nat_1,fc2_membered,fc3_margrel1,t1_numerals,t2_subset,t6_boole,t7_boole,t8_boole,d12_margrel1,involutiveness_k11_margrel1,involutiveness_k9_margrel1,redefinition_k11_margrel1,dt_k11_margrel1,dt_k7_margrel1,dt_k8_margrel1,dt_k9_margrel1,fc4_margrel1,rc2_margrel1,d13_margrel1,d14_margrel1,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,t36_margrel1,t41_margrel1]),
    [interesting(0.5),file(binari_3,e4_6_2_2__binari_3),[file(binari_3,e4_6_2_2__binari_3)]]).

fof(e5_6_2_2__binari_3,plain,(
    1 = k1_funct_1(k4_finseqop(k1_numbers,c1_6__binari_3,1),c1_6_2__binari_3) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6_2__binari_3,dt_c1_6__binari_3,dt_c2_6__binari_3,e1_6_2__binari_3,e2_6_2__binari_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,rc1_margrel1,reflexivity_r1_tarski,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,fc1_margrel1,fc5_membered,fc6_membered,rc1_membered,rc2_nat_1,rc3_nat_1,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_finseq_1,dt_k1_zfmisc_1,dt_k4_finseq_2,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_nat_1,cc2_nat_1,cc4_membered,cc6_membered,cc9_membered,rc1_nat_1,t2_subset,t3_subset,t4_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,redefinition_k2_finseq_1,redefinition_k4_finseqop,dt_k1_funct_1,dt_k1_numbers,dt_k2_finseq_1,dt_k2_finseq_2,dt_k4_finseqop,dt_c1_6__binari_3,dt_c1_6_2__binari_3,cc3_nat_1,fc2_membered,t1_subset,t7_boole,spc1_numerals,spc1_boole,e4_6_2__binari_3,t70_finseq_2]),
    [interesting(0.5),file(binari_3,e5_6_2_2__binari_3),[file(binari_3,e5_6_2_2__binari_3)]]).

fof(e6_6_2__binari_3,plain,(
    k1_funct_1(k6_binarith(c1_6__binari_3,c2_6__binari_3),c1_6_2__binari_3) = k1_funct_1(k4_finseqop(k1_numbers,c1_6__binari_3,1),c1_6_2__binari_3) ),
    inference(iterative_eq,[status(thm),assumptions([e1_6__binari_3,dt_c1_6_2__binari_3,dt_c1_6__binari_3,dt_c2_6__binari_3,e1_6_2__binari_3,e2_6_2__binari_3])],[e1_6_2_2__binari_3,e2_6_2_2__binari_3,e3_6_2_2__binari_3,e4_6_2_2__binari_3,e5_6_2_2__binari_3]),
    [interesting(0.65),file(binari_3,e6_6_2__binari_3),[file(binari_3,e6_6_2__binari_3)]]).

fof(i3_6_2__binari_3,theorem,(
    $true ),
    introduced(tautology,[file(binari_3,i3_6_2__binari_3)]),
    [interesting(0.65),trivial,file(binari_3,i3_6_2__binari_3)]).

fof(i2_6_2__binari_3,plain,(
    k1_funct_1(k6_binarith(c1_6__binari_3,c2_6__binari_3),c1_6_2__binari_3) = k1_funct_1(k4_finseqop(k1_numbers,c1_6__binari_3,1),c1_6_2__binari_3) ),
    inference(conclusion,[status(thm),assumptions([e1_6__binari_3,dt_c1_6_2__binari_3,dt_c1_6__binari_3,dt_c2_6__binari_3,e1_6_2__binari_3,e2_6_2__binari_3])],[e6_6_2__binari_3,i3_6_2__binari_3]),
    [interesting(0.65),file(binari_3,i2_6_2__binari_3),[file(binari_3,i2_6_2__binari_3)]]).

fof(i1_6_2__binari_3,plain,
    ( ( r1_xreal_0(1,c1_6_2__binari_3)
      & r1_xreal_0(c1_6_2__binari_3,k3_finseq_1(k6_binarith(c1_6__binari_3,c2_6__binari_3))) )
   => k1_funct_1(k6_binarith(c1_6__binari_3,c2_6__binari_3),c1_6_2__binari_3) = k1_funct_1(k4_finseqop(k1_numbers,c1_6__binari_3,1),c1_6_2__binari_3) ),
    inference(discharge_asm,[status(thm),assumptions([e1_6__binari_3,dt_c1_6_2__binari_3,dt_c1_6__binari_3,dt_c2_6__binari_3]),discharge_asm(discharge,[e1_6_2__binari_3,e2_6_2__binari_3])],[e1_6_2__binari_3,e2_6_2__binari_3,i2_6_2__binari_3]),
    [interesting(0.65),file(binari_3,i1_6_2__binari_3),[file(binari_3,i1_6_2__binari_3)]]).

fof(i1_6_2_tmp__binari_3,plain,
    ( m2_subset_1(c1_6_2__binari_3,k1_numbers,k5_numbers)
   => ( ( r1_xreal_0(1,c1_6_2__binari_3)
        & r1_xreal_0(c1_6_2__binari_3,k3_finseq_1(k6_binarith(c1_6__binari_3,c2_6__binari_3))) )
     => k1_funct_1(k6_binarith(c1_6__binari_3,c2_6__binari_3),c1_6_2__binari_3) = k1_funct_1(k4_finseqop(k1_numbers,c1_6__binari_3,1),c1_6_2__binari_3) ) ),
    inference(discharge_asm,[status(thm),assumptions([e1_6__binari_3,dt_c1_6__binari_3,dt_c2_6__binari_3]),discharge_asm(discharge,[dt_c1_6_2__binari_3])],[dt_c1_6_2__binari_3,i1_6_2__binari_3]),
    [interesting(0.8),e3_6__binari_3]).

fof(e3_6__binari_3,plain,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ( ( r1_xreal_0(1,A)
          & r1_xreal_0(A,k3_finseq_1(k6_binarith(c1_6__binari_3,c2_6__binari_3))) )
       => k1_funct_1(k6_binarith(c1_6__binari_3,c2_6__binari_3),A) = k1_funct_1(k4_finseqop(k1_numbers,c1_6__binari_3,1),A) ) ) ),
    inference(let,[status(thm),assumptions([e1_6__binari_3,dt_c1_6__binari_3,dt_c2_6__binari_3])],[i1_6_2_tmp__binari_3,dh_c1_6_2__binari_3]),
    [interesting(0.8),file(binari_3,e3_6__binari_3),[file(binari_3,e3_6__binari_3)]]).

fof(e1_6_1__binari_3,plain,(
    k3_finseq_1(k6_binarith(c1_6__binari_3,c2_6__binari_3)) = c1_6__binari_3 ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__binari_3,dt_c2_6__binari_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,commutativity_k2_tarski,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_k2_tarski,dt_m1_finseq_1,dt_m2_relset_1,fc12_membered,fc13_membered,fc14_membered,fc15_membered,fc16_membered,rc1_margrel1,rc1_nat_1,rc2_margrel1,rc2_nat_1,rc3_nat_1,spc0_boole,spc1_boole,t1_numerals,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m1_subset_1,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_card_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_k6_margrel1,dt_m1_finseq_2,dt_m1_subset_1,dt_m2_finseq_1,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_margrel1,cc1_membered,cc1_nat_1,cc20_membered,cc2_membered,cc2_nat_1,cc3_membered,cc3_nat_1,cc4_membered,cc6_membered,cc9_membered,fc1_margrel1,fc3_margrel1,fc5_membered,fc6_membered,rc1_membered,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset,d12_margrel1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseq_2,dt_k5_numbers,dt_k6_binarith,dt_m2_finseq_2,dt_m2_subset_1,dt_c1_6__binari_3,dt_c2_6__binari_3,cc15_membered,fc2_membered,t6_boole,t7_boole,t8_boole,t109_finseq_2]),
    [interesting(0.65),file(binari_3,e1_6_1__binari_3),[file(binari_3,e1_6_1__binari_3)]]).

fof(t69_finseq_2,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : k3_finseq_1(k2_finseq_2(A,B)) = A ) ),
    file(finseq_2,t69_finseq_2),
    [interesting(0.9),axiom,file(finseq_2,t69_finseq_2)]).

fof(e2_6_1__binari_3,plain,(
    c1_6__binari_3 = k3_finseq_1(k4_finseqop(k1_numbers,c1_6__binari_3,1)) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_6__binari_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,reflexivity_r1_tarski,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,rc1_margrel1,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k1_zfmisc_1,dt_k5_ordinal2,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc6_membered,cc9_membered,fc1_margrel1,fc5_membered,fc6_membered,rc1_membered,rc2_nat_1,rc3_nat_1,t1_subset,t3_subset,t4_subset,t5_subset,existence_m1_subset_1,existence_m2_finseq_2,existence_m2_subset_1,redefinition_k5_numbers,redefinition_m2_finseq_2,redefinition_m2_subset_1,dt_k1_card_1,dt_k4_finseq_2,dt_k5_numbers,dt_m1_subset_1,dt_m2_finseq_2,dt_m2_subset_1,cc10_membered,cc11_membered,cc15_membered,cc1_nat_1,cc2_nat_1,cc4_membered,rc1_nat_1,t2_subset,t6_boole,t7_boole,t8_boole,redefinition_k3_finseq_1,redefinition_k4_finseqop,dt_k1_numbers,dt_k2_finseq_2,dt_k3_finseq_1,dt_k4_finseqop,dt_c1_6__binari_3,cc3_nat_1,fc2_membered,spc1_numerals,spc1_boole,t69_finseq_2]),
    [interesting(0.65),file(binari_3,e2_6_1__binari_3),[file(binari_3,e2_6_1__binari_3)]]).

fof(e2_6__binari_3,plain,(
    k3_finseq_1(k6_binarith(c1_6__binari_3,c2_6__binari_3)) = k3_finseq_1(k4_finseqop(k1_numbers,c1_6__binari_3,1)) ),
    inference(iterative_eq,[status(thm),assumptions([dt_c2_6__binari_3,dt_c1_6__binari_3])],[e1_6_1__binari_3,e2_6_1__binari_3]),
    [interesting(0.8),file(binari_3,e2_6__binari_3),[file(binari_3,e2_6__binari_3)]]).

fof(t18_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( k3_finseq_1(A) = k3_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(1,C)
                      & r1_xreal_0(C,k3_finseq_1(A)) )
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    file(finseq_1,t18_finseq_1),
    [interesting(0.9),axiom,file(finseq_1,t18_finseq_1)]).

fof(e4_6__binari_3,plain,(
    k6_binarith(c1_6__binari_3,c2_6__binari_3) = k4_finseqop(k1_numbers,c1_6__binari_3,1) ),
    inference(mizar_by,[status(thm),assumptions([e1_6__binari_3,dt_c2_6__binari_3,dt_c1_6__binari_3])],[existence_m1_relset_1,dt_k2_zfmisc_1,dt_m1_relset_1,cc1_relset_1,existence_m1_finseq_1,existence_m2_relset_1,redefinition_m2_relset_1,dt_m1_finseq_1,dt_m2_relset_1,fc14_membered,fc15_membered,rc1_margrel1,commutativity_k2_tarski,reflexivity_r1_tarski,antisymmetry_r2_hidden,existence_m1_finseq_2,existence_m2_finseq_1,redefinition_m2_finseq_1,dt_k1_xboole_0,dt_k2_tarski,dt_m1_finseq_2,dt_m2_finseq_1,cc12_membered,cc13_membered,cc14_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc3_nat_1,fc12_membered,fc13_membered,fc16_membered,fc1_margrel1,fc6_membered,rc1_membered,rc1_nat_1,rc2_margrel1,rc2_nat_1,rc3_nat_1,t1_subset,t2_real,t3_real,t4_subset,t5_real,t5_subset,t6_real,t7_real,t8_real,existence_m1_subset_1,existence_m2_finseq_2,redefinition_m2_finseq_2,dt_k1_card_1,dt_k1_zfmisc_1,dt_k2_finseq_2,dt_k4_finseq_2,dt_k5_ordinal2,dt_k6_margrel1,dt_m1_subset_1,dt_m2_finseq_2,cc10_membered,cc11_membered,cc15_membered,cc16_membered,cc17_membered,cc1_margrel1,cc1_nat_1,cc2_nat_1,cc4_membered,cc6_membered,cc9_membered,fc3_margrel1,fc5_membered,t1_numerals,t1_real,t2_subset,t3_subset,t4_real,t6_boole,t7_boole,t8_boole,d12_margrel1,reflexivity_r1_xreal_0,connectedness_r1_xreal_0,existence_m2_subset_1,redefinition_k3_finseq_1,redefinition_k4_finseqop,redefinition_k5_numbers,redefinition_m2_subset_1,dt_k1_funct_1,dt_k1_numbers,dt_k3_finseq_1,dt_k4_finseqop,dt_k5_numbers,dt_k6_binarith,dt_m2_subset_1,dt_c1_6__binari_3,dt_c2_6__binari_3,fc2_membered,rqLessOrEqual__r1_xreal_0__r1_r0,spc0_numerals,spc1_numerals,spc0_boole,spc1_boole,e3_6__binari_3,e2_6__binari_3,t18_finseq_1,rqLessOrEqual__r1_xreal_0__r1_r1,rqLessOrEqual__r1_xreal_0__r0_r1,rqLessOrEqual__r1_xreal_0__r0_r0]),
    [interesting(0.8),file(binari_3,e4_6__binari_3),[file(binari_3,e4_6__binari_3)]]).

fof(i4_6__binari_3,theorem,(
    $true ),
    introduced(tautology,[file(binari_3,i4_6__binari_3)]),
    [interesting(0.8),trivial,file(binari_3,i4_6__binari_3)]).

fof(i3_6__binari_3,plain,(
    k6_binarith(c1_6__binari_3,c2_6__binari_3) = k4_finseqop(k1_numbers,c1_6__binari_3,1) ),
    inference(conclusion,[status(thm),assumptions([e1_6__binari_3,dt_c2_6__binari_3,dt_c1_6__binari_3])],[e4_6__binari_3,i4_6__binari_3]),
    [interesting(0.8),file(binari_3,i3_6__binari_3),[file(binari_3,i3_6__binari_3)]]).

fof(i2_6__binari_3,plain,
    ( c2_6__binari_3 = k5_euclid(c1_6__binari_3)
   => k6_binarith(c1_6__binari_3,c2_6__binari_3) = k4_finseqop(k1_numbers,c1_6__binari_3,1) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c2_6__binari_3,dt_c1_6__binari_3]),discharge_asm(discharge,[e1_6__binari_3])],[e1_6__binari_3,i3_6__binari_3]),
    [interesting(0.8),file(binari_3,i2_6__binari_3),[file(binari_3,i2_6__binari_3)]]).

fof(i2_6_tmp__binari_3,plain,
    ( m2_finseq_2(c2_6__binari_3,k6_margrel1,k4_finseq_2(c1_6__binari_3,k6_margrel1))
   => ( c2_6__binari_3 = k5_euclid(c1_6__binari_3)
     => k6_binarith(c1_6__binari_3,c2_6__binari_3) = k4_finseqop(k1_numbers,c1_6__binari_3,1) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_6__binari_3]),discharge_asm(discharge,[dt_c2_6__binari_3])],[dt_c2_6__binari_3,i2_6__binari_3]),
    [interesting(0.8),i1_6__binari_3]).

fof(i1_6__binari_3,plain,(
    ! [A] : 
      ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(c1_6__binari_3,k6_margrel1))
     => ( A = k5_euclid(c1_6__binari_3)
       => k6_binarith(c1_6__binari_3,A) = k4_finseqop(k1_numbers,c1_6__binari_3,1) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_6__binari_3])],[i2_6_tmp__binari_3,dh_c2_6__binari_3]),
    [interesting(0.8),file(binari_3,i1_6__binari_3),[file(binari_3,i1_6__binari_3)]]).

fof(i1_6_tmp__binari_3,plain,
    ( m2_subset_1(c1_6__binari_3,k1_numbers,k5_numbers)
   => ! [A] : 
        ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(c1_6__binari_3,k6_margrel1))
       => ( A = k5_euclid(c1_6__binari_3)
         => k6_binarith(c1_6__binari_3,A) = k4_finseqop(k1_numbers,c1_6__binari_3,1) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_6__binari_3])],[dt_c1_6__binari_3,i1_6__binari_3]),
    [interesting(1),t6_binari_3]).

fof(t6_binari_3,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
         => ( B = k5_euclid(A)
           => k6_binarith(A,B) = k4_finseqop(k1_numbers,A,1) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_6_tmp__binari_3,dh_c1_6__binari_3]),
    [interesting(1),file(binari_3,t6_binari_3),[file(binari_3,t6_binari_3)]]).