pc A (mk_qpowerclass ? (B ∩ C) (mem_ok' ? (intersect_ok ? B C)))
≡ intersect ? (pc ? B) (pc ? C).
+unification hint 1 ≔
+ A : setoid, B,C : qpowerclass A;
+ DX ≟ (intersect ? (pc ? B) (pc ? C)),
+ SX ≟ (mk_qpowerclass ? (B ∩ C) (mem_ok' ? (intersect_ok ? B C)))
+ (*-----------------------------------------------------------------*) ⊢
+ pc A SX ≡ DX.
+
nlemma intersect_ok': ∀A. binary_morphism1 (powerclass_setoid A) (powerclass_setoid A) (powerclass_setoid A).
#A; @ (λS,S'. S ∩ S');
#a; #a'; #b; #b'; *; #Ha1; #Ha2; *; #Hb1; #Hb2; @; #x; nnormalize; *; #Ka; #Kb; @