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).

Lemma monoW : {mono f : x / aP x >-> rP x} -> {homo f : x / aP x >-> rP x}.