Section Proper.
Let U := Type.
Context {A B : U}.
Class Proper (R : relation A) (m : A) : Prop :=
proper_prf : R m m.
(** Every element in the carrier of a reflexive relation is a morphism for this relation.  We use a proxy class for this case which is used internally to discharge reflexivity constraints.  The [Reflexive] instance will almost always be used, but it won't apply in general to any kind of [Proper (A -> B) _ _] goal, making proof-search much slower. A cleaner solution would be to be able to set different priorities in different hint bases and select a particular hint database for resolution of a type class constraint. *)
Class ProperProxy (R : relation A) (m : A) : Prop :=
proper_proxy : R m m.

Lemma eq_proper_proxy (x : A) : ProperProxy (@eq A) x.