proposition: Lemma unitrMr x y : x \is a unit -> (x * y \is a unit) = (y \is a unit).
proof: Proof. move=> Ux; apply/idP/idP=> [Uxy | Uy]; last by rewrite unitrMl. by rewrite -(mulKr Ux y) unitrMl ?unitrV. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)