(* in a sorted list, the last element is maximal *)
(* and the maximal element is last *)

(* Specifications: *)
Lemma sorted_last_key_max (A : ordType) (s : seq A) x y :
sorted oleq s -> x \in s -> oleq x (last y s).
Lemma sorted_max_key_last (A : ordType) (s : seq A) x y :
sorted oleq s -> x \in s ->
(forall z, z \in s -> oleq z x) -> last y s = x.
Lemma seq_last_mono (A : ordType) (s1 s2 : seq A) x :
path oleq x s1 -> path oleq x s2 ->
{subset s1 <= s2} ->
oleq (last x s1) (last x s2).