Instance add_compat2 (A : Type) x dom :
  Proper (Logic.eq ==> @eq A dom dom ==> @eq A (Dom.add x dom) (Dom.add x dom)) (@add A dom x).

Theorem remove_compat : forall A x y dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂), X.eq x y -> eq m₁ m₂ -> eq (remove x m₁) (remove y m₂).