proposition: Lemma double_monotone2 a b: natp a -> natp b -> (cdouble a <c cdouble b <-> a <c b).
proof: Proof. move => aN bN; split. move => [/(double_monotone aN bN) sa sb]; split => // h; case: sb; ue. move =>[/(double_monotone aN bN) sa sb]; split => //. by move /(double_inj aN bN). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)