(* -------------------------------------------------------------------------- *)
ntheorem prove_huntingtons_axiom:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀add:∀_:Univ.∀_:Univ.Univ.
∀b:Univ.
∀H2:eq Univ (negate d) c.
∀H3:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
-∀H5:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b)
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#add.
-#b.
-#c.
-#d.
-#negate.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-nauto by H0,H1,H2,H3,H4,H5;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#b ##.
+#c ##.
+#d ##.
+#negate ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+nauto by H0,H1,H2,H3,H4,H5 ##;
nqed.
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