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

Theorem eq_remove : forall A x (E F : gen_env A),
ok E -> ok F ->
E ≍ F ->
E ∖ {x} ≍ F ∖ {x}.