(* ----Denial of equation E3 *)
ntheorem prove_e3:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀b:Univ.
∀complement:∀_:Univ.Univ.
∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).
∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
∀H8:∀X:Univ.eq Univ (meet (complement X) X) n0.
-∀H9:∀X:Univ.eq Univ (join (complement X) X) n1.eq Univ (join (complement (join (join (meet (complement a) b) (meet (complement a) (complement b))) (meet a (join (complement a) b)))) (join (complement a) b)) n1
+∀H9:∀X:Univ.eq Univ (join (complement X) X) n1.eq Univ (join (complement (join (join (meet (complement a) b) (meet (complement a) (complement b))) (meet a (join (complement a) b)))) (join (complement a) b)) n1)
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#complement.
-#join.
-#meet.
-#n0.
-#n1.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#complement ##.
+#join ##.
+#meet ##.
+#n0 ##.
+#n1 ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##;
nqed.
(* -------------------------------------------------------------------------- *)