% Mizar problem: t49_isomichi,isomichi,1288,36 
fof(t49_isomichi,conjecture,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_isomichi(B,A)
          <=> v4_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_xboole_0,cc10_isomichi,cc11_isomichi,cc12_isomichi,cc13_isomichi,cc14_isomichi,cc15_isomichi,cc1_isomichi,cc2_isomichi,cc3_isomichi,cc4_isomichi,cc5_isomichi,cc6_isomichi,cc7_isomichi,cc8_isomichi,cc9_isomichi,d7_isomichi,d8_xboole_0,dt_k1_tops_1,dt_k1_zfmisc_1,dt_k3_subset_1,dt_k6_pre_topc,dt_l1_pre_topc,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_pre_topc,existence_l1_struct_0,existence_m1_subset_1,fc2_tops_1,fc3_tops_1,fc4_isomichi,fc4_tops_1,fc5_isomichi,fc6_isomichi,fc6_tops_1,fc7_isomichi,involutiveness_k3_subset_1,irreflexivity_r2_xboole_0,rc1_tops_1,rc2_isomichi,rc2_tops_1,rc3_isomichi,rc7_isomichi,reflexivity_r1_tarski,t31_subset_1,t3_subset,t3_tdlat_3,t4_tdlat_3]),
    [file(isomichi,t49_isomichi)]).

fof(antisymmetry_r2_xboole_0,axiom,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
     => ~ r2_xboole_0(B,A) ) ),
    file(xboole_0,r2_xboole_0),
    []).

fof(cc10_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v4_pre_topc(B,A)
              & v4_tops_1(B,A) )
           => ( v4_pre_topc(B,A)
              & v5_tops_1(B,A) ) ) ) ) ),
    file(isomichi,cc10_isomichi),
    []).

fof(cc11_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v3_isomichi(B,A)
           => ( ~ v4_isomichi(B,A)
              & ~ v5_isomichi(B,A) ) ) ) ) ),
    file(isomichi,cc11_isomichi),
    []).

fof(cc12_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_isomichi(B,A)
           => ( ~ v3_isomichi(B,A)
              & ~ v5_isomichi(B,A) ) ) ) ) ),
    file(isomichi,cc12_isomichi),
    []).

fof(cc13_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_isomichi(B,A)
           => ( ~ v3_isomichi(B,A)
              & ~ v4_isomichi(B,A) ) ) ) ) ),
    file(isomichi,cc13_isomichi),
    []).

fof(cc14_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_isomichi(B,A)
           => ( v3_isomichi(B,A)
              & ~ v4_isomichi(B,A)
              & ~ v5_isomichi(B,A) ) ) ) ) ),
    file(isomichi,cc14_isomichi),
    []).

fof(cc15_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_isomichi(B,A)
           => ( v3_isomichi(B,A)
              & ~ v4_isomichi(B,A)
              & ~ v5_isomichi(B,A) ) ) ) ) ),
    file(isomichi,cc15_isomichi),
    []).

fof(cc1_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_tops_1(B,A)
           => ( v1_isomichi(B,A)
              & v2_isomichi(B,A) ) ) ) ) ),
    file(isomichi,cc1_isomichi),
    []).

fof(cc2_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v1_isomichi(B,A)
              & v2_isomichi(B,A) )
           => v4_tops_1(B,A) ) ) ) ),
    file(isomichi,cc2_isomichi),
    []).

fof(cc3_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_isomichi(B,A)
           => v1_decomp_1(B,A) ) ) ) ),
    file(isomichi,cc3_isomichi),
    []).

fof(cc4_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_decomp_1(B,A)
           => v2_isomichi(B,A) ) ) ) ),
    file(isomichi,cc4_isomichi),
    []).

fof(cc5_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
           => v3_pre_topc(B,A) ) ) ) ),
    file(isomichi,cc5_isomichi),
    []).

fof(cc6_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
           => v4_pre_topc(B,A) ) ) ) ),
    file(isomichi,cc6_isomichi),
    []).

fof(cc7_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v6_tops_1(B,A)
           => ( v3_pre_topc(B,A)
              & v4_tops_1(B,A)
              & v1_decomp_1(B,A)
              & v1_isomichi(B,A)
              & v2_isomichi(B,A) ) ) ) ) ),
    file(isomichi,cc7_isomichi),
    []).

fof(cc8_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( v3_pre_topc(B,A)
              & v4_tops_1(B,A) )
           => ( v3_pre_topc(B,A)
              & v6_tops_1(B,A) ) ) ) ) ),
    file(isomichi,cc8_isomichi),
    []).

fof(cc9_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v5_tops_1(B,A)
           => ( v4_pre_topc(B,A)
              & v4_tops_1(B,A)
              & v1_decomp_1(B,A)
              & v1_isomichi(B,A)
              & v2_isomichi(B,A) ) ) ) ) ),
    file(isomichi,cc9_isomichi),
    []).

fof(d7_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_isomichi(B,A)
          <=> r2_xboole_0(k6_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k6_pre_topc(A,B))) ) ) ) ),
    file(isomichi,d7_isomichi),
    []).

fof(d8_xboole_0,axiom,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        & A != B ) ) ),
    file(xboole_0,d8_xboole_0),
    []).

fof(dt_k1_tops_1,axiom,(
    ! [A,B] : 
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k1_tops_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(tops_1,k1_tops_1),
    []).

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

fof(dt_k3_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)) ) ),
    file(subset_1,k3_subset_1),
    []).

fof(dt_k6_pre_topc,axiom,(
    ! [A,B] : 
      ( ( l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => m1_subset_1(k6_pre_topc(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ),
    file(pre_topc,k6_pre_topc),
    []).

fof(dt_l1_pre_topc,axiom,(
    ! [A] : 
      ( l1_pre_topc(A)
     => l1_struct_0(A) ) ),
    file(pre_topc,l1_pre_topc),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

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

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_pre_topc,axiom,(
    ? [A] : l1_pre_topc(A) ),
    file(pre_topc,l1_pre_topc),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

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

fof(fc2_tops_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v4_pre_topc(k6_pre_topc(A,B),A) ) ),
    file(tops_1,fc2_tops_1),
    []).

fof(fc3_tops_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v4_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v3_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ),
    file(tops_1,fc3_tops_1),
    []).

fof(fc4_isomichi,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v6_tops_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v5_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ),
    file(isomichi,fc4_isomichi),
    []).

fof(fc4_tops_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v3_pre_topc(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v4_pre_topc(k3_subset_1(u1_struct_0(A),B),A) ) ),
    file(tops_1,fc4_tops_1),
    []).

fof(fc5_isomichi,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & v5_tops_1(B,A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v6_tops_1(k3_subset_1(u1_struct_0(A),B),A) ) ),
    file(isomichi,fc5_isomichi),
    []).

fof(fc6_isomichi,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v3_pre_topc(k1_tops_1(A,k6_pre_topc(A,B)),A)
        & v6_tops_1(k1_tops_1(A,k6_pre_topc(A,B)),A) ) ) ),
    file(isomichi,fc6_isomichi),
    []).

fof(fc6_tops_1,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => v3_pre_topc(k1_tops_1(A,B),A) ) ),
    file(tops_1,fc6_tops_1),
    []).

fof(fc7_isomichi,axiom,(
    ! [A,B] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A)
        & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
     => ( v4_pre_topc(k6_pre_topc(A,k1_tops_1(A,B)),A)
        & v5_tops_1(k6_pre_topc(A,k1_tops_1(A,B)),A) ) ) ),
    file(isomichi,fc7_isomichi),
    []).

fof(involutiveness_k3_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k3_subset_1(A,k3_subset_1(A,B)) = B ) ),
    file(subset_1,k3_subset_1),
    []).

fof(irreflexivity_r2_xboole_0,axiom,(
    ! [A,B] : ~ r2_xboole_0(A,A) ),
    file(xboole_0,r2_xboole_0),
    []).

fof(rc1_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_pre_topc(B,A) ) ) ),
    file(tops_1,rc1_tops_1),
    []).

fof(rc2_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v4_tops_1(B,A)
          & v1_isomichi(B,A)
          & v2_isomichi(B,A) ) ) ),
    file(isomichi,rc2_isomichi),
    []).

fof(rc2_tops_1,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_pre_topc(B,A)
          & v4_pre_topc(B,A) ) ) ),
    file(tops_1,rc2_tops_1),
    []).

fof(rc3_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v5_tops_1(B,A)
          & v6_tops_1(B,A) ) ) ),
    file(isomichi,rc3_isomichi),
    []).

fof(rc7_isomichi,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & v3_isomichi(B,A)
          & ~ v4_isomichi(B,A)
          & ~ v5_isomichi(B,A) ) ) ),
    file(isomichi,rc7_isomichi),
    []).

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

fof(t31_subset_1,axiom,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_tarski(B,C)
          <=> r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B)) ) ) ) ),
    file(subset_1,t31_subset_1),
    []).

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

fof(t3_tdlat_3,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k6_pre_topc(A,k3_subset_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k1_tops_1(A,B)) ) ) ),
    file(tdlat_3,t3_tdlat_3),
    []).

fof(t4_tdlat_3,axiom,(
    ! [A] : 
      ( ( v2_pre_topc(A)
        & l1_pre_topc(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k6_pre_topc(A,B)) ) ) ),
    file(tdlat_3,t4_tdlat_3),
    []).