% Mizar problem: t61_funct_5,funct_5,1550,5 
fof(t61_funct_5, conjecture,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (k1_card_1(A)=k1_card_1(C) & k1_card_1(B)=k1_card_1(D))  => k1_card_1(k1_funct_2(A, B))=k1_card_1(k1_funct_2(C, D))) ) ) ) ) ).
fof(d4_wellord2, axiom,  (! [A] :  (! [B] :  (r2_wellord2(A, B) <=>  (? [C] :  ( (v1_relat_1(C) & v1_funct_1(C))  &  (v2_funct_1(C) &  (k9_xtuple_0(C)=A & k10_xtuple_0(C)=B) ) ) ) ) ) ) ).
fof(dt_k10_xtuple_0, axiom, $true).
fof(dt_k1_card_1, axiom,  (! [A] : v1_card_1(k1_card_1(A))) ).
fof(dt_k1_funct_2, axiom, $true).
fof(dt_k9_xtuple_0, axiom, $true).
fof(projectivity_k1_card_1, axiom,  (! [A] : k1_card_1(k1_card_1(A))=k1_card_1(A)) ).
fof(rc1_funct_1, axiom,  (? [A] :  (v1_relat_1(A) & v1_funct_1(A)) ) ).
fof(rc2_funct_1, axiom,  (? [A] :  (v1_relat_1(A) &  (v1_funct_1(A) & v2_funct_1(A)) ) ) ).
fof(redefinition_r2_wellord2, axiom,  (! [A, B] :  (r2_wellord2(A, B) <=> r3_tarski(A, B)) ) ).
fof(reflexivity_r2_wellord2, axiom,  (! [A, B] : r2_wellord2(A, A)) ).
fof(symmetry_r2_wellord2, axiom,  (! [A, B] :  (r2_wellord2(A, B) => r2_wellord2(B, A)) ) ).
fof(t5_card_1, axiom,  (! [A] :  (! [B] :  (r2_wellord2(A, B) <=> k1_card_1(A)=k1_card_1(B)) ) ) ).
fof(t60_funct_5, axiom,  (! [A] :  (! [B] :  (! [C] :  (! [D] :  ( (r2_wellord2(A, C) & r2_wellord2(B, D))  =>  (r2_wellord2(k1_funct_2(A, B), k1_funct_2(C, D)) & k1_card_1(k1_funct_2(A, B))=k1_card_1(k1_funct_2(C, D))) ) ) ) ) ) ).
