% Mizar problem: t11_projdes1,projdes1,569,7 
fof(t11_projdes1, conjecture,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_collsp(A) &  (v3_collsp(A) &  (v4_collsp(A) &  (v2_anproj_2(A) &  (v3_anproj_2(A) &  ( ~ (v7_anproj_2(A))  & l1_collsp(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ~ ( ( ~ (r1_collsp(A, B, C, D))  &  (r1_projdes1(A, B, C, D, E) &  (r1_projdes1(A, B, C, D, F) &  (r1_projdes1(A, B, C, D, G) &  (r1_projdes1(A, B, C, D, H) &  (! [I] :  (m1_subset_1(I, u1_struct_0(A)) =>  ~ ( (r1_collsp(A, E, F, I) & r1_collsp(A, G, H, I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d1_projdes1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_collsp(A) &  (v3_collsp(A) &  (v4_collsp(A) &  (v2_anproj_2(A) &  (v3_anproj_2(A) &  ( ~ (v7_anproj_2(A))  & l1_collsp(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (r1_projdes1(A, B, C, D, E) <=>  (? [F] :  (m1_subset_1(F, u1_struct_0(A)) &  (r1_collsp(A, B, C, F) & r1_collsp(A, D, E, F)) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_l1_collsp, axiom,  (! [A] :  (l1_collsp(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_collsp, axiom,  (? [A] : l1_collsp(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(rc2_anproj_2, axiom,  (? [A] :  (l1_collsp(A) &  ( ~ (v2_struct_0(A))  &  (v2_collsp(A) &  (v3_collsp(A) &  (v4_collsp(A) &  (v2_anproj_2(A) & v3_anproj_2(A)) ) ) ) ) ) ) ).
fof(t8_projdes1, axiom,  (! [A] :  ( ( ~ (v2_struct_0(A))  &  (v2_collsp(A) &  (v3_collsp(A) &  (v4_collsp(A) &  (v2_anproj_2(A) &  (v3_anproj_2(A) &  ( ~ (v7_anproj_2(A))  & l1_collsp(A)) ) ) ) ) ) )  =>  (! [B] :  (m1_subset_1(B, u1_struct_0(A)) =>  (! [C] :  (m1_subset_1(C, u1_struct_0(A)) =>  (! [D] :  (m1_subset_1(D, u1_struct_0(A)) =>  (! [E] :  (m1_subset_1(E, u1_struct_0(A)) =>  (! [F] :  (m1_subset_1(F, u1_struct_0(A)) =>  (! [G] :  (m1_subset_1(G, u1_struct_0(A)) =>  (! [H] :  (m1_subset_1(H, u1_struct_0(A)) =>  ( (r1_projdes1(A, B, C, D, E) &  (r1_projdes1(A, B, C, D, F) &  (r1_projdes1(A, B, C, D, G) & r1_projdes1(A, B, C, D, H)) ) )  =>  (r1_collsp(A, B, C, D) | r1_projdes1(A, E, F, G, H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
