proposition: Lemma cle_ltT b a c: a <=c b -> b <c c -> a <c c.
proof: Proof. move=> ab [bc nbc]; split; first by exact: (cleT ab bc). by dneg ca; rewrite ca in ab; apply: cleA. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)