intros.
elim H;intro q;intro.
elim H0;intro q';intro.
rewrite H1;rewrite H2.
exists (q'-q).
rewrite (mult_comm d q');rewrite (mult_comm d q);rewrite (mult_comm d (q'-q));auto with arith.
Qed.

(** here we show that if b | a then it is possible to compute q such that a = b*q *)
Lemma quo_dec : forall (a b:nat),(divides a b)->{q:nat | a=b*q}.
intros.