Definition CoPrime (a b : nat) := gcd (Z_of_nat a) (Z_of_nat b) 1.

Lemma uniqueRem :
forall r1 r2 b : nat,
b > 0 ->
forall a : nat,
(exists q : nat, a = q * b + r1 /\ b > r1) ->
(exists q : nat, a = q * b + r2 /\ b > r2) -> r1 = r2.