(* ---- (AB = C) and (AC = B) and -(wv = v). *)
ntheorem prove_there_exists_a_happy_bird:
- ∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.
+ (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.
∀a:Univ.
∀b:Univ.
∀c:Univ.
∀response:∀_:Univ.∀_:Univ.Univ.
∀H0:eq Univ (response a c) b.
∀H1:eq Univ (response a b) c.
-∀H2:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).∃V:Univ.∃W:Univ.eq Univ (response W V) V
+∀H2:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).∃V:Univ.∃W:Univ.eq Univ (response W V) V)
.
-#Univ.
-#V.
-#W.
-#X.
-#Y.
-#a.
-#b.
-#c.
-#compose.
-#response.
-#H0.
-#H1.
-#H2.
-napply ex_intro[
-nid2:
-napply ex_intro[
-nid2:
-nauto by H0,H1,H2;
-nid|
-skip]
-nid|
-skip]
+#Univ ##.
+#V ##.
+#W ##.
+#X ##.
+#Y ##.
+#a ##.
+#b ##.
+#c ##.
+#compose ##.
+#response ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1,H2 ##;
+##| ##skip ##]
+##| ##skip ##]
nqed.
(* -------------------------------------------------------------------------- *)