proposition: Lemma Nint_ccP1 x: (inc x (interval_cc Nat_order a b) <-> (a <=c x /\ x <=c b)).
proof: Proof. apply: (iff_trans (Nint_ccP x)); split. by move=> [[_ _ pa] [_ _ pb]]. move=> [ax bx]; move:(NS_le_nat bx bN) => xN //. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)