(** * Study of the class of weakly monotonic functions (Lemma 2.3) *)
Require Export Monotonic.
Set Implicit Arguments.
Section Global.
Variable A: Type.
Section A.
Variables X Y: Type.
Variable TX: reduction_t A X.
Variable TY: reduction_t A Y.

(* Specifications: *)
(** weak monotonicity entails monotonicity *)
Lemma monotonic_wmonotonic: forall F, monotonic TX TY F -> wmonotonic TX TY F.
(** transitive, reflexive closure respects weak monotonicity *)
Lemma star_wmon: wmonotonic TX TX (star (X:=X)).
Variables F G: function X Y.