End ROOTED1.
Section INVARIANT2.

Lemma invariant2_ind :
forall s0 : Site,
s0 <> owner ->
forall (c : Config) (t : class_trans c),
legal c ->
st c s0 = sigma_rooted s0 (bm c) ->
st (transition c t) s0 = sigma_rooted s0 (bm (transition c t)).