(* -------------------------------------------------------------------------- *)
ntheorem prove_u_combinator:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀apply:∀_:Univ.∀_:Univ.Univ.
∀f:∀_:Univ.Univ.
∀g:∀_:Univ.Univ.
∀k:Univ.
∀s:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Z:Univ.eq Univ (apply (apply Z (f Z)) (g Z)) (apply (g Z) (apply (apply (f Z) (f Z)) (g Z)))
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Z:Univ.eq Univ (apply (apply Z (f Z)) (g Z)) (apply (g Z) (apply (apply (f Z) (f Z)) (g Z))))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#apply.
-#f.
-#g.
-#k.
-#s.
-#H0.
-#H1.
-napply ex_intro[
-nid2:
-nauto by H0,H1;
-nid|
-skip]
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#f ##.
+#g ##.
+#k ##.
+#s ##.
+#H0 ##.
+#H1 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1 ##;
+##| ##skip ##]
nqed.
(* -------------------------------------------------------------------------- *)