proposition: Lemma mono_in_leif (A : {pred T}) (f : T -> T) C : {in A &, {mono f : x y / x <= y}} -> {in A &, forall x y, (f x <= f y ?= iff C) = (x <= y ?= iff C)}.
proof: Proof. by move=> mf x y Ax Ay; rewrite /leif !eq_le !mf. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat choice seq) mathcomp(path fintype tuple bigop finset div prime finfun) mathcomp(finset)