Section INVARIANT6_bis.
(* these two lemmas are just negations of the previous ones *)
(* the parent of a node cannot be the which receives a gp for the first time *)
(* the ancestor of a node cannot be the which receives a gp for the first time *)

Lemma inc_dec_in_append1 :
forall (s0 : Site) (q1 q2 : queue Message),
inc_dec_in_queue s0 (append Message q1 q2) ->
inc_dec_in_queue s0 (append Message q1 (input Message copy q2)).