proposition: Fact trans : transitive le.
proof: Proof. rewrite /le => y x z /andP [] hxy ? /andP [] /(le_trans hxy) ->. by apply: le_trans. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)