More on well founded sets

We prove in this module the lemma:
Lemma wf_coarser:
  (A:Set)
   (R,S:A->A->Prop)
     (coarser A R S)->
       (well_founded A S)->
          (well_founded A R).
Which we use in the module generation to prove the termination of our chain generation algorithm.

As a first step, we build a term Prop_wfi, a Prop clone of well_founded_induction (see the module Wf in $COQTH/INIT).

Exercise

The proof of prop_wfi is trivial; write a simple proof of wf_coarser which does not use this lemma.