proposition: Lemma mulf_eq0 x y : (x * y == 0) = (x == 0) || (y == 0).
proof: Proof. apply/eqP/idP; first exact: mulf_eq0_subproof. by case/pred2P=> ->; rewrite (mulr0, mul0r). Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)