(* Copied from RamifyCoq project *)
Require Export Coq.Relations.Relations.
Require Export Coq.Classes.Equivalence.
Require Coq.Setoids.Setoid.
Definition full_relation {A} : relation A := fun _ _ => True.
Instance same_relation_Equivalence {A}: Equivalence (same_relation A).
Instance inclusion_proper {A}: Proper (same_relation A ==> same_relation A ==> iff) (inclusion A).

Lemma app_same_relation: forall {A: Type} (R1 R2: relation A) (a1 a2: A),
same_relation A R1 R2 ->
(R1 a1 a2 <-> R2 a1 a2).