Lemma parent_invariant_inductive_optim1 : forall (c : Config) (t : class_trans c) (s1 s2 : Site) (q : queue Message) (n : s1 <> s2) (e : bm c s1 owner = input Message dec (input Message (inc_dec s2) q)), legal c -> (legal c -> forall s : Site, indirect_son1 c s -> exists s0 : Site, direct_son c s0 /\ ancestor c s0 s) -> legal (transition c (redirect_inc c s1 s2 q n e)) -> forall s : Site, indirect_son1 (transition c (redirect_inc c s1 s2 q n e)) s -> exists s0 : Site, direct_son (transition c (redirect_inc c s1 s2 q n e)) s0 /\ ancestor (transition c (redirect_inc c s1 s2 q n e)) s0 s.