(** A relation is well-founded if every element is accessible *)

 Definition well_founded := forall a:A, Acc a.

(* Specifications: *)
Theorem well_founded_induction_type : forall P:A -> Type, (forall x:A, (forall y:A, R y x -> P y) -> P x) -> forall a:A, P a.
Theorem well_founded_induction : forall P:A -> Set, (forall x:A, (forall y:A, R y x -> P y) -> P x) -> forall a:A, P a.
Theorem well_founded_ind : forall P:A -> Prop, (forall x:A, (forall y:A, R y x -> P y) -> P x) -> forall a:A, P a.