Section Properties.
Implicit Types x y : TVar.
Implicit Types xs ys : list TVar.
(* ---------------------------------------------------------------------- *)
(** **** Abstract properties of ok *)
(* ---------------------------------------------------------------------- *)
(** **** Properties of binds *)

Theorem binds_update_inv : forall A x (v : A) (F G : gen_env A),
x ∹ v ⋲ (F ::= G) ->
(x ∉ G ∧ x ∹ v ⋲ F) ∨ (x ∈ F ∧ x ∹ v ⋲ G).