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

Theorem binds_update_one_inv : forall A x y (v w : A) (F : gen_env A),
x ∹ v ⋲ (F [y <- w]) ->
(x <> y ∧ x ∹ v ⋲ F) ∨ (x ∈ F ∧ x = y ∧ v = w).