proposition: Lemma coprime_diff a b: natp b -> coprime a (b +c a) -> coprime a b.
proof: Proof. move => bN [aN baN h]; split => // x xa xc. exact:(h _ xa (proj1 (cdivides_sum xc xa))). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)