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