proposition: Lemma coprimer_dvdr a b c : a %| b -> coprimer c b -> coprimer c a.
proof: Proof. move=> dvd_ab cbc; apply: gcdr_def; rewrite ?dvd1r //= => d dc da. by rewrite -(eqd_dvdr _ cbc) dvdr_gcd andbC (dvdr_trans da). 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