(* ------------------------------------------------------------------------------ *)
ntheorem prove_H2:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀b:Univ.
∀c:Univ.
∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.
∀H7:∀X:Univ.eq Univ (join X X) X.
-∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c)))))
+∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c))))))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#c.
-#join.
-#meet.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#join ##.
+#meet ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##;
nqed.
(* ------------------------------------------------------------------------------ *)