proposition: Lemma Sperner_22 A: inc A (free_subsets r) -> cardinal A = cn -> exists k, [/\ natp k, is_half_n n k & A = subsets_with_p_elements k E].
proof: Proof. move / free_rep_prop1 => [f fp <-]; move: (Sperner_cf15 fp). rewrite - (card_bijection (proj31 fp)) (card_nat (proj32 fp)); apply. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)