Proof using.
intros. unfold contiguous_range_exact_lo in *. intuition.
assert (i < S (eIndex b) <= eIndex a).
simpl in *. intuition. specialize (H0 b). concludes. intuition.
specialize (H1 (S (eIndex b))). concludes.
break_exists. simpl In in *. intuition; subst.
- auto.
- omega.
- simpl in *. intuition. specialize (H x). concludes. omega.
Qed.

(* Specifications: *)
Lemma cons_contiguous_sorted :
forall l i a,
sorted (a :: l) ->
contiguous_range_exact_lo (a :: l) i ->
contiguous_range_exact_lo l i.