proposition: Lemma unitmP (x y : M) : reflect (x == 1 /\ y == 1) (x * y == 1).
proof: Proof. by apply: (iffP eqP)=> [/unitm[-> ->]|[/eqP-> /eqP->]] //; rewrite mulm1. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path choice finset fintype finfun) mathcomp(tuple bigop ssralg ssrint ssrnum) xfinmap