proposition: Lemma coprimer_mulr a b c : coprimer a (b * c) = coprimer a b && coprimer a c.
proof: Proof. case/boolP: (coprimer a b) => co_pm /=. by rewrite /coprimer; apply: congr_eqd; rewrite // euclid_gcdl. apply: contraNF co_pm=> cabc. apply: gcdr_def; rewrite ?dvd1r // => x xa xb. by rewrite -(eqd_dvd (eqdd _) cabc) dvdr_gcd xa dvdr_mulr. Qed.
imports: HB(structures) Coq(ssreflect ssrfun ssrbool Arith.Wf_nat) mathcomp(eqtype ssrnat div seq path) mathcomp(ssralg fintype perm tuple choice generic_quotient) mathcomp(matrix bigop zmodp mxalgebra poly) stronglydiscrete