repeat rewrite <- N2Nat.inj_mul; apply le_Nle; repeat rewrite N2Nat.id; auto.
apply lt_Nlt; repeat rewrite N2Nat.id; auto.
Qed.

Theorem Nmult_ge_compat_rev_l: forall n m p , p * n >= p * m -> 0 < p -> n >= m.
intros n m p H1 H2; apply Nge_ge; apply mult_ge_compat_rev_l with (nat_of_N p).