Proof using.
intros. unfold contiguous_range_exact_lo in *. intuition.
specialize (H1 a).
specialize (H0 (S i)).
assert (H_a: In a [a]) by auto with datatypes.
concludes.
assert (H_s: i < S i) by auto.
concludes.
break_exists.
break_and.
inversion H0; subst; auto.
inversion H2.
Qed.

(* Specifications: *)
Lemma contiguous_index_adjacent :
forall l i a b,
sorted (a :: b :: l) ->
contiguous_range_exact_lo (a :: b :: l) i ->
eIndex a = S (eIndex b) /\ eIndex a > i.