Definition AE_type := ProdType (ProdType (ProdType
  (ConstType (share * val * gname * val * val * val * hist))
  (ArrowType (ConstType hist) (ArrowType (ConstType val) Mpred)))
  (ArrowType (ConstType (list AE_hist_el)) (ArrowType (ConstType val) Mpred)))
  (ArrowType (ConstType hist) (ArrowType (ConstType val) Mpred)).

Lemma AE_loc_join : forall sh1 sh2 sh l p g i R h1 h2 (Hjoin : sepalg.join sh1 sh2 sh) (Hsh1 : readable_share sh1) (Hsh2 : readable_share sh2) (Hcompat : disjoint h1 h2), AE_loc sh1 l p g i R h1 * AE_loc sh2 l p g i R h2 = AE_loc sh l p g i R (map_add h1 h2).