Proof using.
set_up_input_handlers;
auto using locks_correct_unlock_sent_lock,
locks_correct_unlock_true_to_false,
locks_correct_true_at_head_of_queue.
Qed.

(* Specifications: *)
Lemma locks_correct_locked_input_handlers_new :
forall h i sigma u st' out ms p,
InputHandler h i (sigma h) = (u, out, st', ms) ->
In (pDst p, pBody p) ms ->
locks_correct_locked (update name_eq_dec sigma h st') p.
Lemma locks_correct_locked_input_handlers_new :
forall h i sigma u st' out ms p,
InputHandler h i (sigma h) = (u, out, st', ms) ->
In (pDst p, pBody p) ms ->
locks_correct_locked (update name_eq_dec sigma h st') p.