Definition tp_wd (f: memren) (tp : t) : Prop :=
forall i (cnti: containsThread tp i),
ctl_wd f (getThreadC cnti).

Lemma ctl_inj_id:
forall f c,
ctl_wd f c ->
(forall b1 b2, f b1 = Some b2 -> b1 = b2) ->
ctl_inj f c c.