proposition: Lemma rpredMl x y : x \in S -> x \is a unit-> (x * y \in S) = (y \in S).
proof: Proof. move=> Sx Ux; apply/idP/idP=> [Sxy | /(rpredM _ _ Sx)-> //]. by rewrite -(mulKr Ux y); rewrite rpredM ?rpredV. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)