proposition: Lemma map_finer_in A : A \in P -> map_finer A \in Q.
proof: Proof. move=> AinP; rewrite /map_finer. case (boolP (A \in P)) => [H |]; last by rewrite AinP. by case: (sig2W _) => /= B. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(div ssralg ssrint ssrnum binomial) tools combclass sorted ordtype partition