Section MonoHomoMorphismTheory.
Variables (aT rT sT : Type) (f : aT -> rT) (g : rT -> aT).
Variables (aP : pred aT) (rP : pred rT) (aR : rel aT) (rR : rel rT).

(* Specifications: *)
Lemma monoW : {mono f : x / aP x >-> rP x} -> {homo f : x / aP x >-> rP x}.
Lemma monoLR :
{mono f : x y / aR x y >-> rR x y} -> forall x y, rR (f x) y = aR x (g y).
Lemma monoLR_in :
{in aD &, {mono f : x y / aR x y >-> rR x y}} ->
{in aD & rD, forall x y, rR (f x) y = aR x (g y)}.