Definition newer (l : hist_part) t := forall t', l t' <> None -> (t' < t)%nat.

Lemma add_new_inj : forall h h' t t' v v' (Ht : newer h t) (Ht' : newer h' t'),
map_upd h t v = map_upd h' t' v' -> h = h' /\ t = t' /\ v = v'.