proposition: Lemma zchinese_remainder x y : (x == y %[mod m1 * m2])%Z = (x == y %[mod m1])%Z && (x == y %[mod m2])%Z.
proof: Proof. by rewrite !eqz_mod_dvd Gauss_dvdz. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime order) mathcomp(ssralg poly ssrnum ssrint archimedean rat matrix) mathcomp(polydiv perm zmodp mxalgebra vector)