Proof using.
unfold locks_correct_locked.
intuition. congruence.
Qed.

Lemma locks_correct_locked_input_handlers_old :
forall h i sigma u st' out ms p,
InputHandler h i (sigma h) = (u, out, st', ms) ->
locks_correct sigma ->
locks_correct_locked sigma p ->
locks_correct_locked (update name_eq_dec sigma h st') p.