End Well_founded.
Set Implicit Arguments.
(** Reasoning about well-founded fixpoints on measures. *)
Section Measure_well_founded.
(* Measure relations are well-founded if the underlying relation is well-founded. *)
Variables T M: Type.
Variable R: M -> M -> Prop.
Hypothesis wf: well_founded R.
Variable m: T -> M.
Definition MR (x y: T): Prop := R (m x) (m y).
Register MR as program.wf.mr.

(* Specifications: *)
Lemma measure_wf: well_founded MR.
Proof with auto.