Inductive deprecated_Euclid : Set :=
    deprecated_Euclid_intro :
    forall u v d:Z, u * a + v * b = d -> Zis_gcd a b d -> deprecated_Euclid.Inductive deprecated_Euclid : Set :=
    deprecated_Euclid_intro :
    forall u v d:Z, u * a + v * b = d -> Zis_gcd a b d -> deprecated_Euclid.

Lemma deprecated_euclid_rec : forall v3:Z, 0 <= v3 -> forall u1 u2 u3 v1 v2:Z, u1 * a + u2 * b = u3 -> v1 * a + v2 * b = v3 -> (forall d:Z, Zis_gcd u3 v3 d -> Zis_gcd a b d) -> deprecated_Euclid.