intros n; case n; clear n.
intros.
apply le_n.
intros.
inversion_clear H.
intros m ih n H.
inversion_clear H.
apply le_n.
apply le_S.
apply ih; assumption.
Qed.

Lemma eq_lt_trans : forall n m p : nat, n = m -> m < p -> n < p.
intros n m p eq lt.