∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
-∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (inverse (inverse a)) a
+∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (inverse (inverse a)) a)
∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
-∀H3:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply a (inverse a) b) b
+∀H3:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply a (inverse a) b) b)
∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
-∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply a (inverse a) b) b
+∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply a (inverse a) b) b)
∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y (inverse Y)) X.
∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y (inverse Y)) X.
∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
-∀H3:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply y x x) x
+∀H3:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply y x x) x)
∀H7:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X (inverse X)) Y) Y.
∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y.
∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.
∀H7:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X (inverse X)) Y) Y.
∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y.
∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.
-∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) (add (multiply Y Z) (multiply Z X))) (multiply (add X Y) (multiply (add Y Z) (add Z X))).eq Univ (multiply a (add b c)) (add (multiply b a) (multiply c a))
+∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) (add (multiply Y Z) (multiply Z X))) (multiply (add X Y) (multiply (add Y Z) (add Z X))).eq Univ (multiply a (add b c)) (add (multiply b a) (multiply c a)))
∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X (inverse X)) Y) Y.
∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y.
∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.
∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X (inverse X)) Y) Y.
∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y.
∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X.
-∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) (add (multiply Y Z) (multiply Z X))) (multiply (add X Y) (multiply (add Y Z) (add Z X))).eq Univ (inverse (inverse a)) a
+∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) (add (multiply Y Z) (multiply Z X))) (multiply (add X Y) (multiply (add Y Z) (add Z X))).eq Univ (inverse (inverse a)) a)
∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
-∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c)) b
+∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c)) b)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply (multiply d e a) b (multiply d e c)) (multiply d e (multiply a b c))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply (multiply d e a) b (multiply d e c)) (multiply d e (multiply a b c)))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply b a a) a
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply b a a) a)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply a b (inverse b)) a
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply a b (inverse b)) a)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply a a b) a
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply a a b) a)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply (inverse b) b a) a
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (multiply (multiply A (inverse A) B) (inverse (multiply (multiply C D E) F (multiply C D G))) (multiply D (multiply G F E) C)) B.eq Univ (multiply (inverse b) b a) a)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add b a) (add a b)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add b a) (add a b))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add (add a b) c) (add a (add b c))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add (add a b) c) (add a (add b c)))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B A))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B A))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand A B))) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand C (nand A B))) C.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B C))) (nand C (nand A B))) C.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B B))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand A (nand B B))) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B B)) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B B)) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand C (nand A B))) C.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand B C)) A) (nand C (nand A B))) C.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand A (nand A B)) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) A) A) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand A C))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand (nand (nand A B) C) C) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a))
∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).
-∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b)))
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.
∀apply:∀_:Univ.∀_:Univ.Univ.
∀k:Univ.
∀s:Univ.
∀x:Univ.
∀y:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y) (apply y (apply (apply x x) y))
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y) (apply y (apply (apply x x) y)))
∀H0:eq Univ strong_fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply k (apply (apply s s) (apply s k)))) (apply (apply s (apply k s)) k))).
∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.
∀strong_fixed_point:Univ.
∀H0:eq Univ strong_fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply k (apply (apply s s) (apply s k)))) (apply (apply s (apply k s)) k))).
∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.
-∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)))
∀H0:eq Univ strong_fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply (apply s (apply k s)) k)) (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))).
∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.
∀strong_fixed_point:Univ.
∀H0:eq Univ strong_fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply (apply s (apply k s)) k)) (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))).
∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.
-∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)))
∀H0:eq Univ strong_fixed_point (apply (apply s (apply k (apply (apply (apply s s) (apply (apply s k) k)) (apply (apply s s) (apply s k))))) (apply (apply s (apply k s)) k)).
∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.
∀strong_fixed_point:Univ.
∀H0:eq Univ strong_fixed_point (apply (apply s (apply k (apply (apply (apply s s) (apply (apply s k) k)) (apply (apply s s) (apply s k))))) (apply (apply s (apply k s)) k)).
∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X.
-∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)))
∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply h (apply (apply b (apply (apply b h) (apply b b))) (apply h (apply (apply b h) (apply b b))))) h)) b)) b).
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply h X) Y) Z) (apply (apply (apply X Y) Z) Y).
∀strong_fixed_point:Univ.
∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply h (apply (apply b (apply (apply b h) (apply b b))) (apply h (apply (apply b h) (apply b b))))) h)) b)) b).
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply h X) Y) Z) (apply (apply (apply X Y) Z) Y).
-∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)))
∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply (apply b b) n)) n))) n)) b)) b).
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).
∀strong_fixed_point:Univ.
∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply (apply b b) n)) n))) n)) b)) b).
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).
-∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)))
∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply n (apply b b))) n))) n)) b)) b).
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).
∀strong_fixed_point:Univ.
∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply (apply b b) (apply (apply n (apply n (apply b b))) n))) n)) b)) b).
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).
-∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)))
∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply (apply b b) n))))) n)) b)) b).
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).
∀strong_fixed_point:Univ.
∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply (apply b b) n))))) n)) b)) b).
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).
-∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)))
∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply n (apply b b)))))) n)) b)) b).
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).
∀strong_fixed_point:Univ.
∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply n (apply b b)))))) n)) b)) b).
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).
-∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)))
-∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).∃U:Univ.eq Univ (response U (f U)) (response a (response b (response c (f U))))
+∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).∃U:Univ.eq Univ (response U (f U)) (response a (response b (response c (f U)))))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t b)) (apply (apply b b) t)) x) y) z) (apply y (apply x z))
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t b)) (apply (apply b b) t)) x) y) z) (apply y (apply x z)))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t b)) b)) t) x) y) z) (apply y (apply x z))
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t b)) b)) t) x) y) z) (apply y (apply x z)))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) b)) x) y) z) (apply x (apply z y))
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) b)) x) y) z) (apply x (apply z y)))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) b) x) y) z) (apply x (apply z y))
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) b) x) y) z) (apply x (apply z y)))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)) x) y) z) (apply (apply x z) y)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)) x) y) z) (apply (apply x z) y))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) t) x) y) z) (apply (apply x z) y)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) t) x) y) z) (apply (apply x z) y))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z y) x)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z y) x))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) (apply (apply b b) t)) x) y) z) (apply (apply z y) x)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) (apply (apply b b) t)) x) y) z) (apply (apply z y) x))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z y) x)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z y) x))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) (apply (apply b b) b))) t) x) y) z) (apply (apply z y) x)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) (apply (apply b b) b))) t) x) y) z) (apply (apply z y) x))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z x) y)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z x) y))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b b) t)) x) y) z) (apply (apply z x) y)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b b) t)) x) y) z) (apply (apply z x) y))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z x) y)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z x) y))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) b))) t) x) y) z) (apply (apply z x) y)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) b))) t) x) y) z) (apply (apply z x) y))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) b)) t) x) y) z) (apply (apply z x) y)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) b)) t) x) y) z) (apply (apply z x) y))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b t) t))) x) y) z) (apply (apply z x) y)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b t) t))) x) y) z) (apply (apply z x) y))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b t) t)) x) y) z) (apply (apply z x) y)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b t) t)) x) y) z) (apply (apply z x) y))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
∀y:Univ.
∀z:Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) t)) t)) x) y) z) (apply (apply z x) y)
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) t)) t)) x) y) z) (apply (apply z x) y))
-∀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))
-∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a (multiply a a)) identity
+∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a (multiply a a)) identity)
-∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply identity a) a
+∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply identity a) a)
-∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a identity) a
+∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a identity) a)
-∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c))
+∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c)))
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply a (multiply a (multiply a a))) identity
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply a (multiply a (multiply a a))) identity)
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply identity a) a
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply identity a) a)
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply a identity) a
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply a identity) a)
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c))
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply Y (multiply (multiply Y (multiply (multiply Y Y) (multiply X Z))) (multiply Z (multiply Z Z)))) X.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c)))
-∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (greatest_lower_bound b c)) (greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c))
+∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (greatest_lower_bound b c)) (greatest_lower_bound (least_upper_bound a b) (least_upper_bound a c)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#c.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##;
-∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (least_upper_bound b c)) (least_upper_bound (greatest_lower_bound a b) (greatest_lower_bound a c))
+∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (least_upper_bound b c)) (least_upper_bound (greatest_lower_bound a b) (greatest_lower_bound a c)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#c.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##;
-∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply b c))
+∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply b c)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#c.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##;
-∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply a c))
+∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply a c)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#c.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##;
-∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d)))
+∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d))))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#c.
-#d.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#d ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##;
-∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d)))
+∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d))))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#c.
-#d.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#d ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##;
-∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a (multiply b c)) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))
+∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a (multiply b c)) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#c.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-#H16.
-#H17.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##;
-∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a (multiply b c)) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))) (greatest_lower_bound a (multiply b c))
+∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a (multiply b c)) (multiply (greatest_lower_bound a b) (greatest_lower_bound a c))) (greatest_lower_bound a (multiply b c)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#c.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-#H16.
-#H17.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##;
-∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (multiply (least_upper_bound a identity) (least_upper_bound b identity))
+∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (multiply (least_upper_bound a identity) (least_upper_bound b identity)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##;
-∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (multiply (least_upper_bound a identity) (least_upper_bound b identity))
+∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (multiply (least_upper_bound a identity) (least_upper_bound b identity)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-#H16.
-#H17.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##;
-∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (least_upper_bound (multiply a b) identity)
+∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (least_upper_bound (multiply a b) identity))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##;
-∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (least_upper_bound (multiply a b) identity)
+∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (least_upper_bound (multiply a b) identity))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-#H16.
-#H17.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##;
-∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (inverse (greatest_lower_bound a (inverse b))))
+∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (inverse (greatest_lower_bound a (inverse b)))))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##;
-∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (inverse (greatest_lower_bound a (inverse b))))
+∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (inverse (greatest_lower_bound a (inverse b)))))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#greatest_lower_bound.
-#identity.
-#inverse.
-#least_upper_bound.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-#H16.
-#H17.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#greatest_lower_bound ##.
+#identity ##.
+#inverse ##.
+#least_upper_bound ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##;
∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X (multiply Y Y)) (multiply Y (multiply Y X)).
∀a:Univ.
∀b:Univ.
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X (multiply Y Y)) (multiply Y (multiply Y X)).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a b))))))) (multiply a (multiply a (multiply a (multiply a (multiply b (multiply b (multiply b b)))))))
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a b))))))) (multiply a (multiply a (multiply a (multiply a (multiply b (multiply b (multiply b b))))))))
∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X (multiply Y (multiply Y Y))) (multiply Y (multiply Y (multiply Y X))).
∀a:Univ.
∀b:Univ.
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X (multiply Y (multiply Y Y))) (multiply Y (multiply Y (multiply Y X))).
-∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a b))))))))))))))))) (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b b)))))))))))))))))
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a (multiply b (multiply a b))))))))))))))))) (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply a (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b (multiply b b))))))))))))))))))
-∀H0:∀U:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply U (inverse (multiply Y (multiply (multiply (multiply Z (inverse Z)) (inverse (multiply U Y))) U)))) U.eq Univ (multiply x (inverse (multiply y (multiply (multiply (multiply z (inverse z)) (inverse (multiply u y))) x)))) u
+∀H0:∀U:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply U (inverse (multiply Y (multiply (multiply (multiply Z (inverse Z)) (inverse (multiply U Y))) U)))) U.eq Univ (multiply x (inverse (multiply y (multiply (multiply (multiply z (inverse z)) (inverse (multiply u y))) x)))) u)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply (inverse B) C) (inverse (multiply D (multiply A C))))))) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)))
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
-∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1))
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
-∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2)
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
-∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)))
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
-∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1))
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
-∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2)
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
-∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide B B) B) C) (divide (divide (divide B B) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)))
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
-∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1))
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
-∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2)
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
-∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)))
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity)
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply identity a2) a2
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply identity a2) a2)
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)))
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity)
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply identity a2) a2
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply identity a2) a2)
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)))
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (inverse a1) a1) identity
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (inverse a1) a1) identity)
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply identity a2) a2
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply identity a2) a2)
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)))
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply (inverse a1) a1) identity
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply (inverse a1) a1) identity)
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply identity a2) a2
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply identity a2) a2)
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
∀H0:∀A:Univ.eq Univ identity (divide A A).
∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)))
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
∀a2:Univ.
∀b2:Univ.
∀divide:∀_:Univ.∀_:Univ.Univ.
∀inverse:∀_:Univ.Univ.
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
-∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide A A) (divide B (divide (divide C (divide D B)) (inverse D)))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide A A) (divide B (divide (divide C (divide D B)) (inverse D)))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2)
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
∀a2:Univ.
∀b2:Univ.
∀divide:∀_:Univ.∀_:Univ.Univ.
∀inverse:∀_:Univ.Univ.
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
-∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide A (divide B (divide C D)))) (divide (divide D C) A)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide A (divide B (divide C D)))) (divide (divide D C) A)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2)
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
∀a2:Univ.
∀b2:Univ.
∀divide:∀_:Univ.∀_:Univ.Univ.
∀inverse:∀_:Univ.Univ.
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
-∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A B) C) (divide D C))) (divide B A)) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A B) C) (divide D C))) (divide B A)) D.eq Univ (multiply (multiply (inverse b2) b2) a2) a2)
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
∀a2:Univ.
∀b2:Univ.
∀divide:∀_:Univ.∀_:Univ.Univ.
∀inverse:∀_:Univ.Univ.
∀multiply:∀_:Univ.∀_:Univ.Univ.
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
-∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A A) B) (divide C (divide B D)))) D) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A A) B) (divide C (divide B D)))) D) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2)
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply (inverse a1) a1) identity
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply (inverse a1) a1) identity)
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply identity a2) a2
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply identity a2) a2)
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3)))
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity)
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply a b) (multiply b a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity)
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2)
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a)
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
-∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a)
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
∀a:Univ.
∀b:Univ.
∀double_divide:∀_:Univ.∀_:Univ.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.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply a b) (multiply b a)
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
∀a:Univ.
∀b:Univ.
∀double_divide:∀_:Univ.∀_:Univ.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.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply a b) (multiply b a)
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
∀a:Univ.
∀b:Univ.
∀double_divide:∀_:Univ.∀_:Univ.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.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply a b) (multiply b a)
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
∀a:Univ.
∀b:Univ.
∀double_divide:∀_:Univ.∀_:Univ.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.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply a b) (multiply b a)
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
∀a:Univ.
∀b:Univ.
∀double_divide:∀_:Univ.∀_:Univ.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.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply a b) (multiply b a)
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
∀a:Univ.
∀b:Univ.
∀double_divide:∀_:Univ.∀_:Univ.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.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply a b) (multiply b a)
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
∀a:Univ.
∀b:Univ.
∀double_divide:∀_:Univ.∀_:Univ.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.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply a b) (multiply b a)
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply a b) (multiply b a))
∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
∀a:Univ.
∀b:Univ.
∀double_divide:∀_:Univ.∀_:Univ.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.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply a b) (multiply b a)
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply a b) (multiply b a))
∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
∀H8:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.
∀H9:∀X:Univ.eq Univ (join X X) X.
∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
∀H8:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.
∀H9:∀X:Univ.eq Univ (join X X) X.
-∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet (join b c) (join b d))) (meet (meet a (meet (join b c) (join b d))) (join (meet a (join b (meet c d))) (join (meet a c) (meet a d))))
+∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (meet (join b c) (join b d))) (meet (meet a (meet (join b c) (join b d))) (join (meet a (join b (meet c d))) (join (meet a c) (meet a d)))))
∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).
∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
∀H8:∀X:Univ.eq Univ (meet (complement X) X) n0.
∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).
∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
∀H8:∀X:Univ.eq Univ (meet (complement X) X) n0.
-∀H9:∀X:Univ.eq Univ (join (complement X) X) n1.eq Univ (join a (join (meet (complement a) (meet (join a (complement b)) (join a b))) (meet (complement a) (join (meet (complement a) b) (meet (complement a) (complement b)))))) n1
+∀H9:∀X:Univ.eq Univ (join (complement X) X) n1.eq Univ (join a (join (meet (complement a) (meet (join a (complement b)) (join a b))) (meet (complement a) (join (meet (complement a) b) (meet (complement a) (complement b)))))) n1)
∀H9:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
∀H10:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.
∀H11:∀X:Univ.eq Univ (join X X) X.
∀H9:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
∀H10:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.
∀H11:∀X:Univ.eq Univ (join X X) X.
-∀H12:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement b) (join (complement a) (meet (complement b) (join a (meet (complement b) (complement a))))))) (join a (meet (complement b) (join (complement a) (meet (complement b) (join a (meet (complement b) (join (complement a) (meet (complement b) a))))))))
+∀H12:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement b) (join (complement a) (meet (complement b) (join a (meet (complement b) (complement a))))))) (join a (meet (complement b) (join (complement a) (meet (complement b) (join a (meet (complement b) (join (complement a) (meet (complement b) a)))))))))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#complement.
-#join.
-#meet.
-#n0.
-#n1.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#complement ##.
+#join ##.
+#meet ##.
+#n0 ##.
+#n1 ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12 ##;
∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
∀H8:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.
∀H9:∀X:Univ.eq Univ (join X X) X.
∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
∀H8:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.
∀H9:∀X:Univ.eq Univ (join X X) X.
-∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet (join a (complement b)) (join (join (meet a b) (meet (complement a) b)) (meet (complement a) (complement b)))) (join (meet a b) (meet (complement a) (complement b)))
+∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet (join a (complement b)) (join (join (meet a b) (meet (complement a) b)) (meet (complement a) (complement b)))) (join (meet a b) (meet (complement a) (complement b))))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f A (f (f B B) B)) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f A (f (f B B) B)) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f (f B A) A) (f C A)) (f (f A A) D))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f (f B A) A) (f C A)) (f (f A A) D))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f C (f (f A A) C)) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f C (f (f A A) C)) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f B (f A B)) B) (f A (f C (f (f A B) (f (f C C) D))))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b))))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f B (f A B)) B) (f A (f C (f (f A B) (f (f C C) D))))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b)))))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f A A) C) (f (f (f (f (f A B) C) C) A) (f A D)))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f A A) C) (f (f (f (f (f A B) C) C) A) (f A D)))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f A A) C) (f (f (f (f (f A B) C) C) A) (f A D)))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b))))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f B A) (f (f (f A A) C) (f (f (f (f (f A B) C) C) A) (f A D)))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b)))))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f C A)) D) (f A (f (f (f (f (f (f B B) A) C) C) A) B))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f C A)) D) (f A (f (f (f (f (f (f B B) A) C) C) A) B))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f C A)) D) (f A (f (f (f (f (f (f B B) A) C) C) A) B))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b))))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f C A)) D) (f A (f (f (f (f (f (f B B) A) C) C) A) B))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b)))))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f (f B (f B (f (f C C) A))) A) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a)))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f (f B (f B (f (f C C) A))) A) C))) A.eq Univ (f a (f (f b c) (f b c))) (f c (f (f b a) (f b a))))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f (f B (f B (f (f C C) A))) A) C))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b))))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (f (f (f (f B A) (f A C)) D) (f A (f (f (f B (f B (f (f C C) A))) A) C))) A.eq Univ (f a (f b (f a (f c c)))) (f a (f c (f a (f b b)))))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a a) a
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a a) a)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a b) (meet b a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a b) (meet b a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet (meet a b) c) (meet a (meet b c))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet (meet a b) c) (meet a (meet b c)))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a a) a
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a a) a)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a b) (join b a)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a b) (join b a))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join (join a b) c) (join a (join b c))
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join (join a b) c) (join a (join b c)))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a (join a b)) a
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a (join a b)) a)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a (meet a b)) a
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a (meet a b)) a)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a a) a
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a a) a)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet b a) (meet a b)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet b a) (meet a b))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a a) a
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a a) a)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join b a) (join a b)
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join b a) (join a b))
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet (meet (join a b) (join c b)) b) b
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet (meet (join a b) (join c b)) b) b)
-∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join (join (meet a b) (meet c b)) b) b
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join (join (meet a b) (meet c b)) b) b)
∀H20:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
∀H21:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
∀H22:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
∀H20:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
∀H21:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
∀H22:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
-∀H23:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (associator a b c) (associator a c b)) additive_identity
+∀H23:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (associator a b c) (associator a c b)) additive_identity)
.
.
-#Univ.
-#U.
-#V.
-#X.
-#Y.
-#Z.
-#a.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#b.
-#c.
-#commutator.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-#H16.
-#H17.
-#H18.
-#H19.
-#H20.
-#H21.
-#H22.
-#H23.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22,H23;
+#Univ ##.
+#U ##.
+#V ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#b ##.
+#c ##.
+#commutator ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+#H18 ##.
+#H19 ##.
+#H20 ##.
+#H21 ##.
+#H22 ##.
+#H23 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22,H23 ##;
-∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (add (associator (multiply a b) c d) (associator a b (multiply c d))) (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d)))) additive_identity
+∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (add (associator (multiply a b) c d) (associator a b (multiply c d))) (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d)))) additive_identity)
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#b.
-#c.
-#commutator.
-#d.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#b ##.
+#c ##.
+#commutator ##.
+#d ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##;
-∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (add (associator (multiply a b) c d) (associator a b (multiply c d))) (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d)))) additive_identity
+∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (add (associator (multiply a b) c d) (associator a b (multiply c d))) (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d)))) additive_identity)
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#b.
-#c.
-#commutator.
-#d.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-#H16.
-#H17.
-#H18.
-#H19.
-#H20.
-#H21.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#b ##.
+#c ##.
+#commutator ##.
+#d ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+#H18 ##.
+#H19 ##.
+#H20 ##.
+#H21 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##;
∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
∀H10:∀X:Univ.eq Univ (add X additive_identity) X.
∀H11:∀X:Univ.eq Univ (add additive_identity X) X.
∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
-∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity
+∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity)
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#x.
-#y.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#x ##.
+#y ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##;
∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
∀H18:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
∀H19:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
∀H18:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
∀H19:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
-∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity
+∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity)
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#x.
-#y.
-#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 ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#x ##.
+#y ##.
+#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 ##;
∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
∀H10:∀X:Univ.eq Univ (add X additive_identity) X.
∀H11:∀X:Univ.eq Univ (add additive_identity X) X.
∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
-∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (multiply (associator x x y) (associator x x y)) x) (multiply (associator x x y) (associator x x y))) additive_identity
+∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (multiply (associator x x y) (associator x x y)) x) (multiply (associator x x y) (associator x x y))) additive_identity)
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#x.
-#y.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#x ##.
+#y ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##;
∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
∀H18:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
∀H19:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
∀H18:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
∀H19:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
-∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (multiply (multiply (multiply (associator x x y) (associator x x y)) x) (multiply (associator x x y) (associator x x y))) additive_identity
+∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (multiply (multiply (multiply (associator x x y) (associator x x y)) x) (multiply (associator x x y) (associator x x y))) additive_identity)
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#x.
-#y.
-#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 ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#x ##.
+#y ##.
+#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 ##;
∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
∀H10:∀X:Univ.eq Univ (add X additive_identity) X.
∀H11:∀X:Univ.eq Univ (add additive_identity X) X.
∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
-∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (add (add (add (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity
+∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (add (add (add (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity)
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#x.
-#y.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#x ##.
+#y ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##;
∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
∀H18:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
∀H19:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
∀H18:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
∀H19:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
-∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (add (add (add (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity
+∀H20:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).eq Univ (add (add (add (add (add (multiply (associator x x y) (multiply (associator x x y) (associator x x y))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) (multiply (associator x x y) (multiply (associator x x y) (associator x x y)))) additive_identity)
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#x.
-#y.
-#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 ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#x ##.
+#y ##.
+#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 ##;
-∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y))
+∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#w.
-#x.
-#y.
-#z.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#w ##.
+#x ##.
+#y ##.
+#z ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##;
-∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y))
+∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#w.
-#x.
-#y.
-#z.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-#H16.
-#H17.
-#H18.
-#H19.
-#H20.
-#H21.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#w ##.
+#x ##.
+#y ##.
+#z ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+#H18 ##.
+#H19 ##.
+#H20 ##.
+#H21 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##;
-∀H15:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y))
+∀H15:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#w.
-#x.
-#y.
-#z.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#w ##.
+#x ##.
+#y ##.
+#z ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##;
-∀H22:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y))
+∀H22:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (associator (multiply x y) z w) (associator x y (commutator z w))) (add (multiply x (associator y z w)) (multiply (associator x z w) y)))
.
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#w.
-#x.
-#y.
-#z.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-#H13.
-#H14.
-#H15.
-#H16.
-#H17.
-#H18.
-#H19.
-#H20.
-#H21.
-#H22.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#w ##.
+#x ##.
+#y ##.
+#z ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+#H16 ##.
+#H17 ##.
+#H18 ##.
+#H19 ##.
+#H20 ##.
+#H21 ##.
+#H22 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22 ##;