(** we can now define the quotient of a by b in case of b | a *)
Definition quo (a b:nat) (H:(divides a b)) := let (q,_):=(quo_dec a b H) in q.

Lemma quo_mult : forall (a b:nat)(H:divides a b),forall (n:nat),(b<>O)->(quo (a*n) b (divides_mult b a n H))=n*(quo a b H).