(* the ancestor of a node cannot be the which receives a gp for the first time *)

Lemma inc_dec_in_append :
forall (s0 : Site) (q1 q2 q3 q4 : queue Message),
append Message q1 q2 = append Message q3 q4 ->
inc_dec_in_queue s0 (append Message q3 (input Message copy q4)) ->
inc_dec_in_queue s0 (append Message q1 (input Message copy q2)).