proposition: Lemma Nmax_p1 x y: natp x -> natp y -> [/\ natp (cmax x y), x <=c (cmax x y) & y <=c (cmax x y)].
proof: Proof. move => xN yN. have ha : natp (cmax x y) by apply:Gmax_E. by move:(cmax_p1 (CS_nat xN) (CS_nat yN)) => [hb hc]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)