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-(* File : GRP011-4 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : GRP011-4 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Group Theory *)
(* ----There exists an identity element *)
ntheorem prove_left_cancellation:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀b:Univ.
∀c:Univ.
∀d:Univ.
∀H0:eq Univ (multiply b c) (multiply d c).
∀H1:∀X:Univ.eq Univ (multiply (inverse X) X) identity.
∀H2:∀X:Univ.eq Univ (multiply identity X) X.
-∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ b d
+∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ b d)
.
-#Univ.
-#X.
-#Y.
-#Z.
-#b.
-#c.
-#d.
-#identity.
-#inverse.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-nauto by H0,H1,H2,H3;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#b ##.
+#c ##.
+#d ##.
+#identity ##.
+#inverse ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+nauto by H0,H1,H2,H3 ##;
+ntry (nassumption) ##;
nqed.
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