Ltac set_up_input_handlers :=
    intros;
    find_apply_lem_hyp InputHandler_cases;
    intuition idtac; try break_exists; intuition idtac; subst;
    repeat find_rewrite;
    simpl in *; intuition idtac; repeat find_inversion;
    try now rewrite update_nop_ext.

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