simplify.apply eq_f.assumption.
qed.
-(* some problem here: confusion between relations/symmetric
-and functions/symmetric; functions symmetric is not in
-functions.moo why?
-theorem symmetric_plus: symmetric nat plus. *)
-
theorem sym_plus: \forall n,m:nat. n+m = m+n.
intros.elim n.
simplify.apply plus_n_O.
theorem injective_plus_l: \forall m:nat.injective nat nat (\lambda n.n+m).
intro.simplify.intros.
-(* qui vorrei applicare injective_plus_r *)
-apply inj_plus_r m.
+apply injective_plus_r m.
rewrite < sym_plus.
rewrite < sym_plus y.
assumption.