(* -------------------------------------------------------------------------- *)
ntheorem prove_associativity:
- ∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀b:Univ.
∀c:Univ.
∀inverse:∀_:Univ.Univ.
∀multiply:∀_:Univ.∀_:Univ.Univ.
-∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (inverse (multiply (multiply (inverse (multiply (inverse Y) (multiply (inverse X) W))) Z) (inverse (multiply Y Z))))) W.eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c)
+∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (inverse (multiply (multiply (inverse (multiply (inverse Y) (multiply (inverse X) W))) Z) (inverse (multiply Y Z))))) W.eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c))
.
-#Univ.
-#W.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#c.
-#inverse.
-#multiply.
-#H0.
-nauto by H0;
+#Univ ##.
+#W ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#inverse ##.
+#multiply ##.
+#H0 ##.
+nauto by H0 ##;
nqed.
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