proposition: Lemma imset_eq0 (A : {set aT}) : (f @: A == set0) = (A == set0).
proof: Proof. have [-> | [x Ax]] := set_0Vmem A; first by rewrite imset0 !eqxx. by rewrite -!cards_eq0 (cardsD1 x) Ax (cardsD1 (f x)) imset_f. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)