proposition: Lemma coprime_if_bezout a b u v: u * a = v * b + 1 -> coprime a b.
proof: Proof. move => H; apply/coprimeP. by move: H; case:(posnP a) => // ->; rewrite muln0 addn1. by exists (u,v); rewrite /= H addKn. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)