Proof using.
unfold LockServ_network_network_invariant.
intuition; simpl in *; congruence.
Qed.

(* Specifications: *)
Lemma LockServ_nwnw_input_handlers_old_new :
forall h i sigma u st' out ms p p',
InputHandler h i (sigma h) = (u, out, st', ms) ->
locks_correct sigma ->
LockServ_network_invariant sigma p ->
In (pDst p', pBody p') ms ->
pSrc p' = h ->
LockServ_network_network_invariant p p'.
Lemma LockServ_nwnw_input_handlers_old_new :
forall h i sigma u st' out ms p p',
InputHandler h i (sigma h) = (u, out, st', ms) ->
locks_correct sigma ->
LockServ_network_invariant sigma p ->
In (pDst p', pBody p') ms ->
pSrc p' = h ->
LockServ_network_network_invariant p p'.