Definition AccessMap_EI_Property (j:meminj) (m1 m1' m2 : mem)
           (AM:ZMap.t (Z -> perm_kind -> option permission)):Prop :=
  forall b2,
    (Mem.valid_block m2 b2 -> forall k ofs2,
       match j b2 with
         None => PMap.get b2 AM ofs2 k  =
                        PMap.get b2 m2.(Mem.mem_access) ofs2 k
       | Some (b3,d3) =>
          (Mem.perm m1 b2 ofs2 Max Nonempty ->
           PMap.get b2 AM ofs2 k = PMap.get b2 m1'.(Mem.mem_access) ofs2 k)
       /\ (~Mem.perm m1 b2 ofs2 Max Nonempty ->
           PMap.get b2 AM ofs2 k  = PMap.get b2 m2.(Mem.mem_access) ofs2 k)
     end)
  /\ (~ Mem.valid_block m2 b2 -> forall k ofs2,
         (Mem.perm m1' b2 ofs2 Max Nonempty ->
           PMap.get b2 AM ofs2 k = PMap.get b2 m1'.(Mem.mem_access) ofs2 k)
       /\ (~Mem.perm m1' b2 ofs2 Max Nonempty -> PMap.get b2 AM ofs2 k = None)).

Lemma EI_ok: forall (m1 m2 m1':mem) (Ext12: Mem.extends m1 m2) (Fwd1: mem_forward m1 m1') m3 j (Inj23: Mem.inject j m2 m3) m3' (Fwd3: mem_forward m3 m3') j' (Inj13': Mem.inject j' m1' m3') (UnchOn3: Mem.unchanged_on (loc_out_of_reach j m1) m3 m3') (InjInc: inject_incr j j') (injSep: inject_separated j j' m1 m3) (UnchOn1: Mem.unchanged_on (loc_unmapped j) m1 m1') m2' (NB: m2'.(Mem.nextblock)=m1'.(Mem.nextblock)) (CONT: Content_EI_Property j m1 m1' m2 (m2'.(Mem.mem_contents))) (ACCESS: AccessMap_EI_Property j m1 m1' m2 (m2'.(Mem.mem_access))), mem_forward m2 m2' /\ Mem.extends m1' m2' /\ Mem.inject j' m2' m3' /\ Mem.unchanged_on (loc_out_of_bounds m1) m2 m2' /\ Mem.unchanged_on (loc_unmapped j) m2 m2'.