(** We can express recursive equations for [compare] *)

(* Specifications: *)
Lemma compare_xO_xO p q : (p~0 ?= q~0) = (p ?= q).
(** Alternative characterisation of strict order in term of addition *)
Lemma lt_iff_add p q : p < q <-> exists r, p + r = q.
Lemma gt_iff_add p q : p > q <-> exists r, q + r = p.
(** Basic facts about [compare_cont] *)
Theorem compare_cont_refl p c :
compare_cont c p p = c.
Lemma compare_cont_antisym p q c :
CompOpp (compare_cont c p q) = compare_cont (CompOpp c) q p.