Corollary find_dom : forall A x v dom (m : t A dom), find x m = Some v -> Dom.In x dom.

Theorem add_comm : forall A x y v₁ v₂ dom (m : t A dom), ¬X.eq x y -> eq (add y v₂ (add x v₁ m)) (add x v₁ (add y v₂ m)).