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

(* Specifications: *)
Lemma parent_does_not_join :
forall (c0 : Config) (s2 s3 s4 : Site),
legal c0 ->
legal (rec_copy2_trans c0 s2) ->
parent (rec_copy2_trans c0 s2) s3 s4 ->
rt c0 s2 = false ->
first Message (bm c0 owner s2) = value Message copy -> s3 <> s2.
Lemma parent_does_not_join :
forall (c0 : Config) (s2 s3 s4 : Site),
legal c0 ->
legal (rec_copy2_trans c0 s2) ->
parent (rec_copy2_trans c0 s2) s3 s4 ->
rt c0 s2 = false ->
first Message (bm c0 owner s2) = value Message copy -> s3 <> s2.
Lemma parent_does_not_join :
forall (c0 : Config) (s2 s3 s4 : Site),
legal c0 ->
legal (rec_copy2_trans c0 s2) ->
parent (rec_copy2_trans c0 s2) s3 s4 ->
rt c0 s2 = false ->
first Message (bm c0 owner s2) = value Message copy -> s3 <> s2.
Lemma parent_does_not_join :
forall (c0 : Config) (s2 s3 s4 : Site),
legal c0 ->
legal (rec_copy2_trans c0 s2) ->
parent (rec_copy2_trans c0 s2) s3 s4 ->
rt c0 s2 = false ->
first Message (bm c0 owner s2) = value Message copy -> s3 <> s2.