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

Theorem combine_None : forall A B C (f : A -> B -> C) g₁ g₂ dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t B dom₂) x, find x (combine f g₁ g₂ m₁ m₂) = None <-> find x m₁ = None ∧ find x m₂ = None.