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

Theorem all_binds_single_singles_inv :
forall A x y (v w : A) ys (ws : list A),
(x ∶ v) ⊏ (y :: ys ∷ w :: ws) ->
(x = y ∧ v = w) ∨ ((x ∶ v) ⊏ (ys ∷ ws)).