Definition full_relation {A} : relation A := fun _ _ => True.

(* Specifications: *)
Lemma inclusion_full_relation: forall {A} P, inclusion A P full_relation.
Lemma same_relation_spec: forall {A} a1 a2, same_relation A a1 a2 <-> pointwise_relation A (pointwise_relation A iff) a1 a2.
Lemma same_relation_Reflexive {A}: Reflexive (same_relation A).
Lemma same_relation_Symmetric {A}: Symmetric (same_relation A).
Lemma same_relation_Transitive {A}: Transitive (same_relation A).