(* -------------------------------------------------------------------------- *)
-(* File : COL083-1 : TPTP v3.2.0. Released v2.6.0. *)
+(* File : COL083-1 : TPTP v3.7.0. Released v2.6.0. *)
(* Domain : Combinatory Logic *)
(* -------------------------------------------------------------------------- *)
ntheorem prove_birds_are_compatible_1:
- ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.
+ (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.
∀a:Univ.
∀compose:∀_:Univ.∀_:Univ.Univ.
∀mocking_bird:Univ.
∀response:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (response (compose A B) C) (response A (response B C)).
-∀H1:∀A:Univ.eq Univ (response mocking_bird A) (response A A).∃A:Univ.∃B:Univ.eq Univ (response a A) B
+∀H1:∀A:Univ.eq Univ (response mocking_bird A) (response A A).∃A:Univ.∃B:Univ.eq Univ (response a A) B)
.
-#Univ.
-#A.
-#B.
-#C.
-#a.
-#compose.
-#mocking_bird.
-#response.
-#H0.
-#H1.
-napply ex_intro[
-nid2:
-napply ex_intro[
-nid2:
-nauto by H0,H1;
-nid|
-skip]
-nid|
-skip]
+#Univ ##.
+#A ##.
+#B ##.
+#C ##.
+#a ##.
+#compose ##.
+#mocking_bird ##.
+#response ##.
+#H0 ##.
+#H1 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1 ##;
+##| ##skip ##]
+##| ##skip ##]
+ntry (nassumption) ##;
nqed.
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