apply le_antisym; auto.
case (le_or_lt m p); intros H'1; auto with arith.
absurd (n * p < n * m); auto with arith.
rewrite H'0; auto with arith.
case (le_or_lt p m); intros H'1; auto with arith.
absurd (n * m < n * p); auto with arith.
rewrite H'0; auto with arith.
Qed.
Definition natEq : forall n m : nat, {n = m} + {n <> m}.
intros n; elim n.
intros m; case m; auto with arith.
intros n0 H' m; case m; auto with arith.
Defined.

Theorem notEqLt : forall n : nat, 0 < n -> n <> 0.
intros n H'; Contradict H'; auto.