Section Properties.
Implicit Types x y : TVar.
Implicit Types xs ys : list TVar.
(* ---------------------------------------------------------------------- *)
(** *** Primary properties *)
(* ---------------------------------------------------------------------- *)
(** **** Properties of singulars *)
(* ---------------------------------------------------------------------- *)
(** **** Properties of concatenation *)
(* ---------------------------------------------------------------------- *)
(** **** Properties of get *)
(* ---------------------------------------------------------------------- *)
(** **** Properties of dom *)
(* ---------------------------------------------------------------------- *)
(** **** Properties of img *)
(* ---------------------------------------------------------------------- *)
(** **** Properties of belongs *)
(* ---------------------------------------------------------------------- *)
(** **** Properties of all_belongs *)
(* ---------------------------------------------------------------------- *)
(** **** Properties of notin *)
(* ---------------------------------------------------------------------- *)
(** **** Properties of all_notin *)
(* ---------------------------------------------------------------------- *)
(** **** Properties of map *)

Axiom map_single : forall A B (f : A -> B) x (v : A),
map f (x ∶ v) = x ∶ (f v).