(** From this general result, we now describe particular cases of [compare_cont p q c = c'] : - When [c=Eq], this is directly [compare] - When [c<>Eq], we'll show first that [c'<>Eq] - That leaves only 4 lemmas for [c] and [c'] being [Lt] or [Gt] *)

(* Specifications: *)
Theorem compare_cont_Eq p q c :
compare_cont c p q = Eq -> c = Eq.
Lemma compare_cont_Lt_Gt p q :
compare_cont Lt p q = Gt <-> p > q.
Lemma compare_cont_Lt_Lt p q :
compare_cont Lt p q = Lt <-> p <= q.
Lemma compare_cont_Gt_Lt p q :
compare_cont Gt p q = Lt <-> p < q.
Lemma compare_cont_Gt_Gt p q :
compare_cont Gt p q = Gt <-> p >= q.
Lemma compare_cont_Lt_not_Lt p q :
compare_cont Lt p q <> Lt <-> p > q.
Lemma compare_cont_Lt_not_Gt p q :
compare_cont Lt p q <> Gt <-> p <= q.
Lemma compare_cont_Gt_not_Lt p q :
compare_cont Gt p q <> Lt <-> p >= q.
Lemma compare_cont_Gt_not_Gt p q :
compare_cont Gt p q <> Gt <-> p < q.