Hint Resolve f_pred_precise f_pred_positive.

Lemma join_hists_spec : forall h1 h2 i, Zlength h1 = Zlength h2 ->
Znth i (join_hists h1 h2) ([], []) =
(fst (Znth i h1 ([], [])) ++ fst (Znth i h2 ([], [])),
(snd (Znth i h1 ([], [])) ++ snd (Znth i h2 ([], [])))).