Instance find_compat2 (A : Type) dom : Proper (X.eq ==> @eq A dom dom ==> Logic.eq) (@find A dom).

(* Specifications: *)
Theorem set_compat : forall A x y v dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂) (Hin₁ : Dom.In x dom₁) (Hin₂ : Dom.In y dom₂), X.eq x y -> eq m₁ m₂ -> eq (set x v m₁ Hin₁) (set y v m₂ Hin₂).