(** ***  Comparisons over dependent maps  **)

Definition eq {A : Type} dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂) := forall x, find x m₁ = find x m₂.Instance eq_refl : forall A dom, Reflexive (@eq A dom dom).

(* Specifications: *)
Lemma eq_sym : forall A dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂), eq m₁ m₂ -> eq m₂ m₁.
Lemma eq_trans : forall A dom₁ dom₂ dom3 (m₁ : t A dom₁) (m₂ : t A dom₂) (m3 : t A dom3), eq m₁ m₂ -> eq m₂ m3 -> eq m₁ m3.