% Mizar problem: t42_isomichi,isomichi,1196,5 
fof(t42_isomichi, conjecture,  (! [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, k2_pre_topc(A, B))=k1_tops_1(A, k2_pre_topc(A, k1_tops_1(A, B))) | k2_pre_topc(A, k1_tops_1(A, B))=k2_pre_topc(A, k1_tops_1(A, k2_pre_topc(A, B))))  => v3_isomichi(B, A)) ) ) ) ) ).
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))) =>  ( (v3_pre_topc(B, A) & v4_tops_1(B, A))  => v6_tops_1(B, A)) ) ) ) ) ).
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))) =>  (v5_tops_1(B, A) =>  (v4_pre_topc(B, A) & v4_tops_1(B, A)) ) ) ) ) ) ).
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_pre_topc(B, A) & v4_tops_1(B, A))  => v5_tops_1(B, A)) ) ) ) ) ).
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))) =>  (v3_isomichi(B, A) =>  ( ~ (v4_isomichi(B, A))  &  ~ (v5_isomichi(B, A)) ) ) ) ) ) ) ).
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))) =>  (v4_isomichi(B, A) =>  ( ~ (v3_isomichi(B, A))  &  ~ (v5_isomichi(B, A)) ) ) ) ) ) ) ).
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))) =>  (v5_isomichi(B, A) =>  ( ~ (v3_isomichi(B, A))  &  ~ (v4_isomichi(B, A)) ) ) ) ) ) ) ).
fof(cc16_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)) ) ) ) ) ).
fof(cc17_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)) ) ) ) ) ).
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_pre_topc(B, A) => v1_isomichi(B, A)) ) ) ) ) ).
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))) =>  (v4_tops_1(B, A) =>  (v1_isomichi(B, A) & v2_isomichi(B, A)) ) ) ) ) ) ).
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))) =>  ( (v1_isomichi(B, A) & v2_isomichi(B, A))  => v4_tops_1(B, A)) ) ) ) ) ).
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))) =>  (v2_isomichi(B, A) => v1_decomp_1(B, A)) ) ) ) ) ).
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))) =>  (v1_decomp_1(B, A) => v2_isomichi(B, A)) ) ) ) ) ).
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)) ) ) ) ) ).
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))) =>  (v5_tops_1(B, A) => v4_pre_topc(B, A)) ) ) ) ) ).
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))) =>  (v6_tops_1(B, A) =>  (v3_pre_topc(B, A) & v4_tops_1(B, A)) ) ) ) ) ) ).
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)))) ) ).
fof(dt_k1_zfmisc_1, axiom, $true).
fof(dt_k2_pre_topc, axiom,  (! [A, B] :  ( (l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => m1_subset_1(k2_pre_topc(A, B), k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_l1_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) => l1_struct_0(A)) ) ).
fof(dt_l1_struct_0, axiom, $true).
fof(dt_m1_subset_1, axiom, $true).
fof(dt_u1_struct_0, axiom, $true).
fof(existence_l1_pre_topc, axiom,  (? [A] : l1_pre_topc(A)) ).
fof(existence_l1_struct_0, axiom,  (? [A] : l1_struct_0(A)) ).
fof(existence_m1_subset_1, axiom,  (! [A] :  (? [B] : m1_subset_1(B, A)) ) ).
fof(fc1_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(k2_pre_topc(A, B), A)) ) ).
fof(fc5_isomichi, axiom,  (! [A, B] :  ( ( (v2_pre_topc(A) & l1_pre_topc(A))  & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => v6_tops_1(k1_tops_1(A, k2_pre_topc(A, B)), A)) ) ).
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))))  => v5_tops_1(k2_pre_topc(A, k1_tops_1(A, B)), A)) ) ).
fof(fc9_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)) ) ).
fof(projectivity_k1_tops_1, axiom,  (! [A, B] :  ( (l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => k1_tops_1(A, k1_tops_1(A, B))=k1_tops_1(A, B)) ) ).
fof(projectivity_k2_pre_topc, axiom,  (! [A, B] :  ( (l1_pre_topc(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))  => k2_pre_topc(A, k2_pre_topc(A, B))=k2_pre_topc(A, B)) ) ).
fof(rc10_pre_topc, 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)) ) ) ) ).
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)) ) ) ) ).
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)) ) ) ) ) ) ).
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)) ) ) ) ) ).
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)) ) ) ) ) ).
fof(rc6_pre_topc, 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)) ) ) ) ).
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)) ) ) ) ).
fof(reflexivity_r1_tarski, axiom,  (! [A, B] : r1_tarski(A, A)) ).
fof(t16_tops_1, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k1_tops_1(A, B), B)) ) ) ) ).
fof(t18_pre_topc, axiom,  (! [A] :  (l1_pre_topc(A) =>  (! [B] :  (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B, k2_pre_topc(A, B))) ) ) ) ).
fof(t3_subset, axiom,  (! [A] :  (! [B] :  (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) ) ) ).
