(**********************************************************************)
(** * Properties of comparison on binary positive numbers *)

(** First, we express [compare_cont] in term of [compare] *)

Definition switch_Eq c c' :=
 match c' with
  | Eq => c
  | Lt => Lt
  | Gt => Gt
 end.

Lemma compare_xO_xI p q : (p~0 ?= q~1) = switch_Eq Lt (p ?= q).