Section Binary.
Variable (u v a b : nat) (Hu : u <> 0) (Hv : v <> 0) (Huv : is_gcd u v 1).
End Binary.

Theorem CRT_informative n (m v : vec nat n) :
(forall p, vec_pos m p <> 0)
-> (forall p q, p <> q -> is_gcd (vec_pos m p) (vec_pos m q) 1)
-> { w | forall p, rem w (vec_pos m p) = rem (vec_pos v p) (vec_pos m p) }.