proposition: Lemma mem_finsupp f k : (k \in finsupp f) = (f k != default k).
proof: Proof. rewrite /fun_of_fsfun [finsupp]unlock; case: fndP; rewrite ?eqxx //=. by move=> kf; rewrite fsfun_subproof. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrnat eqtype ssrfun seq) mathcomp(choice path finset finfun fintype bigop)