(** [Z_of_comparison] is the injection function for comparison *)
Definition Z_of_comparison (c : comparison) : Z :=
  match c with
  | Lt => -1
  | Eq => 0
  | Gt => 1
  end.

(* Specifications: *)
Lemma Z_of_comparison_bound : forall x, -1 <= Z_of_comparison x <= 1.