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(** * 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_cont_Lt_not_Gt p q : compare_cont Lt p q <> Gt <-> p <= q.