Inductive verify_BezoutZ (a b : Z) : Set :=
Bezout_i :
forall u v : Z, (a * u + b * v)%Z = gcdZ a b -> verify_BezoutZ a b.
Definition Q (a : Z) := forall b : Z, verify_BezoutZ a b.

Theorem chinese_remaindering_theorem :
forall a b x y : Z,
gcdZ a b = 1%Z -> {z : Z | congruentZ z x a /\ congruentZ z y b}.