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

(** All_Binds on singulars. *)
Theorem all_binds_singles_singles : forall A xs ys (vs ws : list A),
xs = ys -> vs = ws ->
(xs ∷ vs) ⊏ (ys ∷ ws).