proposition: Lemma segment_Nat_order n: natp n -> segment Nat_order n = Nint n.
proof: Proof. move=> xN; set_extens t;move /Zo_P => [pa pb];apply:Zo_i => //;last by case: pb. move: pb => [ /Nat_order_leP [tn aa bb] cc]. move: NS0 (cle0x (proj31 bb)) => ha hb. split; first by apply/Nat_order_leP. by split; [ apply/Nat_order_leP | exact ]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)