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 ancestor_does_not_join2 :
forall (c0 : Config) (s1 s2 s3 s4 : Site),
legal c0 ->
legal (rec_copy3_trans c0 s1 s2) ->
ancestor (rec_copy3_trans c0 s1 s2) s3 s4 ->
rt c0 s2 = false ->
first Message (bm c0 s1 s2) = value Message copy -> s3 <> s2.