proposition: Lemma idealr_closedB R S : @idealr_closed R S -> zmod_closed S.
proof: Proof. by case=> S0 _ hS; split=> // x y xS yS; rewrite -mulN1r addrC hS. Qed.
imports: HB(structures) mathcomp(ssreflect eqtype choice ssreflect ssrbool ssrnat) mathcomp(ssrfun seq ssralg generic_quotient)