(** ** Implication *)

Definition rel_impl {A B} (R1 R2: rel A B): rel A B :=
  fun x y => R1 x y -> R2 x y.Global Instance rel_impl_subrel_params:
  Params (@rel_impl) 4.

(* Specifications: *)
Lemma rel_impl_rintro {A B} (R1 R2: rel A B) x y: RIntro (R1 x y -> R2 x y) (rel_impl R1 R2) x y.
Lemma rel_impl_relim {A B} (R1 R2: rel A B) x y: RElim (rel_impl R1 R2) x y (R1 x y) (R2 x y).
Lemma rel_impl_subrel_codomain {A B} (R1 R2: rel A B): Related R2 (rel_impl R1 R2) subrel.