Proof using.
unfold getNextIndex, nextIndex_preserved in *.
intuition.
repeat find_rewrite.
auto.
unfold assoc_default in *.
specialize (H h').
break_match.
- eauto using le_trans.
- omega.
Qed.

(* Specifications: *)
Theorem handleClientRequest_nextIndex_preserved :
forall h st client id c out st' ps,
handleClientRequest h st client id c = (out, st', ps) ->
nextIndex_preserved st st'.