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