proposition: Lemma card_uniform_partition n P D : {in P, forall A, #|A| = n} -> partition P D -> #|D| = #|P| * n.
proof: Proof. by move=> uniP /card_partition->; rewrite -sum_nat_const; apply: eq_bigr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop)