proposition: Lemma unitrP x : reflect (exists y, y * x = 1 /\ x * y = 1) (x \is a unit).
proof: Proof. apply: (iffP idP) => [Ux | []]; last exact: unitrP_subproof. by exists x^-1; rewrite divrr ?mulVr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)