proposition: Lemma imset_partition : partition fP (f @: D) = partition P D.
proof: Proof. suff cov: (cover fP == f @:D) = (cover P == D). by rewrite /partition -imset_trivIset imset0mem cov. by rewrite /fP cover_imset -imset_cover (inj_eq (imset_inj inj_f)). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)