proposition: Lemma mem_reducef f k : k \in reducef f = ojoin f.[? k].
proof: Proof. rewrite inE; case: fndP => [kf|] /=; first by rewrite in_fset_valT. by apply: contraNF; apply: (fsubsetP (fset_sub_val _ _)). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrnat eqtype ssrfun seq) mathcomp(choice path finset finfun fintype bigop)