Definition ZdividesP : forall n m : Z, {Zdivides n m} + {~ Zdivides n m}.

Theorem ZquotientUnique : forall m n q r : Z, n <> 0%Z -> m = (q * n + r)%Z -> (Zabs (q * n) <= Zabs m)%Z -> (Zabs r < Zabs n)%Z -> q = Zquotient m n.