(* these two lemmas are just negations of the previous ones *)

Lemma inc_dec_not_in_post :
forall (b : Bag_of_message) (s0 s1 s2 s3 : Site) (m : Message),
~ inc_dec_in_queue s1 (b s0 owner) ->
(forall s4 : Site, m <> inc_dec s4) ->
~ inc_dec_in_queue s1 (Post_message Message m b s2 s3 s0 owner).