apply div_unic_r with (a := x * y) (b := y) (q1 := q) (q2 := x);
auto with arith.
apply is_div_def; inversion_clear H'; auto with arith.
apply le_lt_trans with (m := r); auto with arith.
Qed.

Lemma le_plus_le : forall a b c d : nat, a <= b -> a + c = b + d -> d <= c.