Corollary wf_table_upd_same : forall T k v i (Hwf : wf_table T) (HT : Zlength T = size)
  (Hi : fst (Znth i T) = k) (Hk : k <> 0), wf_table (upd_Znth i T (k, v)).

Lemma add_fails : forall k v b l H H' (HH : apply_hist H l = Some H') (Hadd : In (HAdd k v b) l) (Hk : H k <> None), b = false.