Instance incl_preorder : forall A dom, PreOrder (@incl A dom dom).Instance eq_incl_compat : forall A dom, PartialOrder (@eq A dom dom) (@incl A dom dom).(** ***  Compatibility Instances  **)

Instance mem_compat (A : Type) dom : Proper (X.eq ==> @eq A dom dom ==> Logic.eq) (@mem A dom).

(* Specifications: *)
Theorem find_compat : forall A x y dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂), X.eq x y -> eq m₁ m₂ -> find x m₁ = find y m₂.