-(* move in sets.ma? *)
-nlemma union_morphism : ∀A.Ω^A ⇒_1 (Ω^A ⇒_1 Ω^A).
-#X; napply (mk_binary_morphism1 … (λA,B.A ∪ B));
-#A1 A2 B1 B2 EA EB; napply pset_ext; #x;
-nchange in match (x ∈ (A1 ∪ B1)) with (?∨?);
-napply (.= (setP ??? x EA)‡#);
-napply (.= #‡(setP ??? x EB)); //;
-nqed.
-
-nlemma union_is_ext: ∀A. 𝛀^A → 𝛀^A → 𝛀^A.
- #S A B; @ (A ∪ B); #x y Exy; @; *; #H1;
-##[##1,3: @; ##|##*: @2 ]
-##[##1,3: napply (. (Exy^-1)╪_1#)
-##|##2,4: napply (. Exy╪_1#)]
-nassumption;
-nqed.
-
-alias symbol "hint_decl" = "hint_decl_Type1".
-unification hint 0 ≔
- A : setoid, B,C : 𝛀^A;
- R ≟ (mk_ext_powerclass ? (B ∪ C) (ext_prop ? (union_is_ext ? B C)))
- (* ----------------------------------------------------------------*) ⊢
- ext_carr A R ≡ union ? (ext_carr ? B) (ext_carr ? C).
-
-unification hint 0 ≔ S:Type[0], A,B:Ω^S;
- MM ≟ mk_unary_morphism1 ??
- (λA.mk_unary_morphism1 ?? (λB.A ∪ B) (prop11 ?? (union_morphism S A)))
- (prop11 ?? (union_morphism S))
- (*-----------------------------------------------------*) ⊢
- fun11 ?? (fun11 ?? MM A) B ≡ A ∪ B.
-
-nlemma union_is_ext_morph:∀A:setoid.𝛀^A ⇒_1 (𝛀^A ⇒_1 𝛀^A).
-#A; napply (mk_binary_morphism1 … (union_is_ext …));
-#x1 x2 y1 y2 Ex Ey; napply (prop11 … (union_morphism A)); nassumption.
-nqed.
-
-unification hint 1 ≔
- AA : setoid, B,C : 𝛀^AA;
- A ≟ carr AA,
- R ≟ (mk_unary_morphism1 ??
- (λS:(*ext_powerclass_setoid AA*)𝛀^AA.
- mk_unary_morphism1 ??
- (λS':(*ext_powerclass_setoid AA*)𝛀^AA.
- mk_ext_powerclass AA (S ∪ S') (ext_prop AA (union_is_ext ? S S')))
- (prop11 ?? (union_is_ext_morph AA S)))
- (prop11 ?? (union_is_ext_morph AA))) ,
- BB ≟ (ext_carr ? B),
- CC ≟ (ext_carr ? C)
- (* ------------------------------------------------------*) ⊢
- ext_carr AA (R B C) ≡ union A BB CC.
-
-