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