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