Section Properties.
Implicit Types x y : TVar.
Implicit Types xs ys : list TVar.
(* ---------------------------------------------------------------------- *)
(** *** Primary properties *)

(** Induction scheme over environments. *)
Axiom env_ind : forall A, forall P : gen_env A -> Prop,
(P (@empty A)) ->
(forall (E : gen_env A) x (v : A), P E -> P (E & (x ∶ v))) ->
(forall (E : gen_env A), P E).