Corollary add_items_trace_mono : forall h la h', add_items_trace h la h' ->
  hists_mono h h'.

Lemma apply_no_write : forall i h l v (Hl : hist_list' h l) (Hv : apply_hist i l = Some v) (Hh : Forall (fun p => ~writes (snd p) v) h), v = i /\ Forall (fun e => forall w, ~writes e w) l.