(** More about [eqb] *)
(**********************************************************************)
(** * 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.

(* Specifications: *)
Lemma compare_cont_spec p q c :
compare_cont c p q = switch_Eq c (p ?= q).