Hint Resolve f_pred_precise f_pred_positive.

Lemma add_item_trace_map : forall h k v i s h' (Hlenh : Zlength h = size)
(Htrace : add_item_trace h k v i s h') (Hk : k <> 0) (Hrepk : repable_signed k) (Hrepv : repable_signed v),
let m' := make_map (upd_Znth i h' (Znth i h ([], []))) in
map_incl (make_map h) m' /\ lookup m' k = Some i /\
if s then get (make_map h) k = None /\ make_map h' = upd_Znth i m' (k, v)
else make_map h' = upd_Znth i m' (k, make_int (value_of_hist (snd (Znth i h' ([], []))))).