proposition: Lemma partitionS P D B : partition P D -> B \in P -> B \subset D.
proof: Proof. by move=> partP BP; rewrite -(cover_partition partP); apply: bigcup_max BP _. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)