(** ** 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.

Lemma rel_impl_subrel_codomain {A B} (R1 R2: rel A B): Related R2 (rel_impl R1 R2) subrel.