proposition: Lemma Sperner_p1 k: k <=c n -> free_subset r (subsets_with_p_elements k E).
proof: Proof. move => h; move: (NS_le_nat h Sperner_p0) => kN. by apply:(Sperner_2). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)