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