proposition: Lemma invr_neq0 x : x != 0 -> x^-1 != 0.
proof: Proof. move=> nx0; case Ux: (x \is a unit); last by rewrite invr_out ?Ux. by apply/eqP=> x'0; rewrite -unitrV x'0 unitr0 in Ux. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)