(** The rewriting system sometimes generates arguments constraints of
  the following form (when rewriting an argument of [arrow_rel] for
  instance), which need to be matched against our relational
  properties stated in terms of [subrel]. *)

Global Instance pointwise_relation_subrel_subrel A B:
  Related (pointwise_relation A (pointwise_relation B impl)) subrel subrel.(** *** [Morphisms.Proper] instances *)

(** Now that we can interpret the relators used in [Morphisms]-style
  relational properties, we can simply hook instances of
  [Morphisms.Proper] into our own database.

  We have to be careful about how this instance works. For one thing,
  we are not interested in going through the whole resolution process
  in [Coq.Classes.Morphisms], but are only interested in recovering
  user-defined instances as-is. Moreover, we want to avoid a loop with
  [solve_morphisms_proper] below, where our library (and hence
  [Related] instances) are used to solve [Proper] queries.
  We can make sure both of those things are avoided by using a
  [normalization_done] hypothesis with our [Proper] query. *)

Global Instance morphisms_proper_related {A} (R: relation A) (a: A):
  (normalization_done -> Proper R a) ->
  Monotonic a R | 10.

Lemma subrelation_subrel {A} (R1 R2: relation A): subrelation R1 R2 -> Related R1 R2 subrel.