Instance eq_equiv : forall A dom, Equivalence (@eq A dom dom).Definition incl {A : Type} dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂) :=
  forall x v, find x m₁ = Some v -> find x m₂ = Some v.Instance incl_refl : forall A dom (m : t A dom), Reflexive (@incl A dom dom).

Lemma incl_trans : forall A dom₁ dom₂ dom3 (m₁ : t A dom₁) (m₂ : t A dom₂) (m3 : t A dom3), incl m₁ m₂ -> incl m₂ m3 -> incl m₁ m3.