(* -------------------------------------------------------------------------- *)
-(* File : COL068-1 : TPTP v3.2.0. Released v1.2.0. *)
+(* File : COL068-1 : TPTP v3.7.0. Released v1.2.0. *)
(* Domain : Combinatory Logic *)
(* -------------------------------------------------------------------------- *)
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.
∀combinator:Univ.
∀s:Univ.
∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#apply.
-#b.
-#combinator.
-#s.
-#H0.
-#H1.
-napply ex_intro[
-nid2:
-nauto by H0,H1;
-nid|
-skip]
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#b ##.
+#combinator ##.
+#s ##.
+#H0 ##.
+#H1 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1 ##;
+##| ##skip ##]
+ntry (nassumption) ##;
nqed.
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