(* ----Denial of conclusion: *)
ntheorem prove_associativity_of_meet:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀b:Univ.
∀c:Univ.
∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet (join X Y) (join Y Z)) Y) Y.
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join (meet X Y) (meet Y Z)) Y) Y.
∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (join X Z))) X.
-∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (meet X Z))) X.eq Univ (meet (meet a b) c) (meet a (meet b c))
+∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (meet X Z))) X.eq Univ (meet (meet a b) c) (meet a (meet b c)))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#c.
-#join.
-#meet.
-#H0.
-#H1.
-#H2.
-#H3.
-nauto by H0,H1,H2,H3;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#join ##.
+#meet ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+nauto by H0,H1,H2,H3 ##;
nqed.
(* -------------------------------------------------------------------------- *)