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

Lemma inc_dec_in_collect :
forall (b : Bag_of_message) (s0 s1 s2 s3 : Site) (m : Message),
first Message (b s1 s2) = value Message m ->
inc_dec_in_queue s3 (b s0 owner) ->
m <> inc_dec s3 ->
inc_dec_in_queue s3 (Collect_message Message b s1 s2 s0 owner).