(* -------------------------------------------------------------------------- *)
-(* File : COL031-1 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : COL031-1 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Combinatory Logic *)
(* -------------------------------------------------------------------------- *)
ntheorem prove_fixed_point:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.
∀apply:∀_:Univ.∀_:Univ.Univ.
∀f:∀_:Univ.Univ.
∀l:Univ.
∀o:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply o X) Y) (apply Y (apply X Y)).
-∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))
+∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))))
.
-#Univ.
-#X.
-#Y.
-#apply.
-#f.
-#l.
-#o.
-#H0.
-#H1.
-napply ex_intro[
-nid2:
-nauto by H0,H1;
-nid|
-skip]
+#Univ ##.
+#X ##.
+#Y ##.
+#apply ##.
+#f ##.
+#l ##.
+#o ##.
+#H0 ##.
+#H1 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1 ##;
+##| ##skip ##]
+ntry (nassumption) ##;
nqed.
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