(* WARNING: Not sure simple_lexprod is useful! *)
Definition simple_lexprod {A: Type} (R1: A -> A -> Prop) (R2: A -> A -> Prop)
(x y: A) : Prop :=
R1 x y \/ x=y /\ R2 x y.

Lemma wellfounded_simple_lexprod:
forall A (R1: A -> A -> Prop) (R2: A -> A -> Prop),
well_founded R1 ->
well_founded R2 ->
well_founded (simple_lexprod R1 R2).