proposition: Lemma unitrMl x y : y \is a unit -> (x * y \is a unit) = (x \is a unit).
proof: Proof. move=> Uy; wlog Ux: x y Uy / x \is a unit => [WHxy|]. by apply/idP/idP=> Ux; first rewrite -(mulrK Uy x); rewrite WHxy ?unitrV. rewrite Ux; apply/unitrP; exists (y^-1 * x^-1). by rewrite -!mulrA mulKr ?mulrA ?mulrK ?divrr ?mulVr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)