(** * 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.

(** weak monotonicity entails monotonicity *)
Lemma monotonic_wmonotonic: forall F, monotonic TX TY F -> wmonotonic TX TY F.