proposition: Lemma Ninto_gleP2 x y: gle (Nint_cco a b) x y <-> [/\ a <=c x, y <=c b & x <=c y].
proof: Proof. split. move/Ninto_gleP=> [] /(Nint_ccP1 aN bN) [pa pb] /(Nint_ccP1 aN bN) [pc pd] pe. done. move => [pa pb pc]; move:(cleT pc pb) (cleT pa pc) => pd pe. by apply/Ninto_gleP; split => //; apply /(Nint_ccP1 aN bN). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)