intros n n1 n2 H' H'0; case (le_or_lt n2 n1); auto.
intros H'1; Contradict H'0; auto.
apply le_not_lt; auto with arith.
Qed.

Theorem le_mult_anti_compatibility :
forall n n1 n2 : nat, 0 < n -> n * n1 <= n * n2 -> n1 <= n2.