proposition: Lemma mulrI_eq0 x y : lreg x -> (x * y == 0) = (y == 0).
proof: Proof. by move=> reg_x; rewrite -{1}(mulr0 x) (inj_eq reg_x). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)