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ntheorem prove_these_axioms_3:
- ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.
+ (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.
∀a3:Univ.
∀b3:Univ.
∀c3:Univ.
∀inverse:∀_:Univ.Univ.
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
-∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide A (inverse (double_divide B C))) (double_divide (inverse B) (inverse (double_divide D (double_divide A D))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide A (inverse (double_divide B C))) (double_divide (inverse B) (inverse (double_divide D (double_divide A D))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)))
.
-#Univ.
-#A.
-#B.
-#C.
-#D.
-#a3.
-#b3.
-#c3.
-#double_divide.
-#inverse.
-#multiply.
-#H0.
-#H1.
-nauto by H0,H1;
+#Univ ##.
+#A ##.
+#B ##.
+#C ##.
+#D ##.
+#a3 ##.
+#b3 ##.
+#c3 ##.
+#double_divide ##.
+#inverse ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+nauto by H0,H1 ##;
nqed.
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