proposition: Lemma total_homo_mono : total aR -> {homo f : x y / aR' x y >-> rR' x y} -> {mono f : x y / aR x y >-> rR x y}.
proof: Proof. move=> /(@total_homo_mono_in D rR_anti) hmf hf => x y. by apply: hmf => // ?? _ _; apply: hf. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool)