proposition: Lemma wf_coarser : forall (A : Set) (R S : A -> A -> Prop), coarser A R S -> well_founded S -> well_founded R.
proof: Proof. unfold well_founded in |- *; intros A R S H H0 a. apply Acc_intro; intros y H1. pattern y in |- *; apply Prop_wfi with A S. exact H0. intros; apply Acc_intro; auto. Qed.