Lemma chRem2 :
forall b1 r1 b2 r2 q : Z,
(0 <= r1)%Z ->
(0 <= r2)%Z ->
(r1 < q)%Z -> (r2 < q)%Z -> (b1 * q + r1)%Z = (b2 * q + r2)%Z -> r1 = r2.