(****************************************************)
End Prop_induction.
Definition coarser (A : Set) (R S : A -> A -> Prop) :=
forall x y : A, R x y -> S x y.

(* Specifications: *)
Lemma wf_coarser :
forall (A : Set) (R S : A -> A -> Prop),
coarser A R S -> well_founded S -> well_founded R.