(* -------------------------------------------------------------------------- *)
ntheorem prove_fixed_point:
- ∀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.
∀v:Univ.
∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply v X) Y) Z) (apply (apply Z X) Y).
∀H1:∀X:Univ.eq Univ (apply m X) (apply X X).
-∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#apply.
-#b.
-#f.
-#m.
-#v.
-#H0.
-#H1.
-#H2.
-napply ex_intro[
-nid2:
-nauto by H0,H1,H2;
-nid|
-skip]
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#b ##.
+#f ##.
+#m ##.
+#v ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1,H2 ##;
+##| ##skip ##]
nqed.
(* -------------------------------------------------------------------------- *)