Definition juicy_mem_alloc (jm: juicy_mem) (lo hi: Z) : juicy_mem * block :=
         (mkJuicyMem (fst (alloc (m_dry jm) lo hi))
                     (after_alloc lo hi (snd (alloc (m_dry jm) lo hi)) (m_phi jm)
                            (juicy_mem_alloc_aux1 _ _ _ _ _ (eq_refl _)))
                     (after_alloc_contents_cohere _ _ _ _ _ (eq_refl _))
                     (after_alloc_access_cohere _ _ _ _ _ (eq_refl _))
                     (after_alloc_max_access_cohere _ _ _ _ _ (eq_refl _))
                     (after_alloc_alloc_cohere _ _ _ _ _ (eq_refl _)),
           snd (alloc (m_dry jm) lo hi)).

(* Specifications: *)
Lemma juicy_mem_alloc_level: forall jm lo hi jm' b, juicy_mem_alloc jm lo hi = (jm', b) -> level jm = level jm'.
Lemma juicy_mem_alloc_succeeds: forall j j' b lo hi, juicy_mem_alloc j lo hi = (j', b) -> (m_dry j', b) = alloc (m_dry j) lo hi.