(* -------------------------------------------------------------------------- *)
-(* File : RNG011-5 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : RNG011-5 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Ring Theory *)
(* ----Middle associator identity *)
ntheorem prove_equality:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀add:∀_:Univ.∀_:Univ.Univ.
∀additive_identity:Univ.
∀H17:∀X:Univ.eq Univ (add additive_identity X) X.
∀H18:∀X:Univ.eq Univ (add X additive_identity) X.
∀H19:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
-∀H20:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (associator a a b) a) (associator a a b)) additive_identity
+∀H20:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (associator a a b) a) (associator a a b)) additive_identity)
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#b.
-#commutator.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-#H16.
-#H17.
-#H18.
-#H19.
-#H20.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#b ##.
+#commutator ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+#H18 ##.
+#H19 ##.
+#H20 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20 ##;
+ntry (nassumption) ##;
nqed.
(* -------------------------------------------------------------------------- *)