proposition: Fact join_def_le x y : join x y = if lt x y then y else x.
proof: Proof. by rewrite join_def lt_def; case: eqP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)