\forall n,m:nat. eq nat (plus n (times n m)) (times n (S m)).
intros.elim n.simplify.reflexivity.
simplify.apply f_equal.rewrite < H.
\forall n,m:nat. eq nat (plus n (times n m)) (times n (S m)).
intros.elim n.simplify.reflexivity.
simplify.apply f_equal.rewrite < H.
-transitivity (plus (plus e m) (times e m)).symmetry.
-apply assoc_plus.transitivity (plus (plus m e) (times e m)).
+transitivity (plus (plus e1 m) (times e1 m)).symmetry.
+apply assoc_plus.transitivity (plus (plus m e1) (times e1 m)).