proposition: Lemma divr_closedM : divr_closed -> mulr_closed S.
proof: Proof. by case=> S1 Sdiv; split=> // x y Sx Sy; rewrite -[y]invrK -[y^-1]mul1r !Sdiv. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)