Definition ContentMap_EFF_ValidBlock_FUN b2 ofs2: memval :=
    if locBlocksSrc nu23 b2
    then if (pubBlocksSrc nu23 b2)
         then match source (local_of nu12) m1 b2 ofs2 with
             Some(b1,ofs1) =>
                 if pubBlocksSrc nu12 b1
                 then inject_memval j12'
                      (ZMap.get ofs1 (PMap.get b1 m1'.(Mem.mem_contents)))
                 else ZMap.get ofs2 (PMap.get b2 m2.(Mem.mem_contents))
           | None => ZMap.get ofs2 (PMap.get b2 m2.(Mem.mem_contents))
            end
         else ZMap.get ofs2 (PMap.get b2 m2.(Mem.mem_contents))
    else match source (as_inj nu12) m1 b2 ofs2 with
             Some(b1,ofs1) => inject_memval j12'
                                (ZMap.get ofs1 (PMap.get b1 m1'.(Mem.mem_contents)))
           | None => ZMap.get ofs2 (PMap.get b2 m2.(Mem.mem_contents))
         end.Definition ContentMap_EFF_InvalidBlock_FUN b2 ofs2: memval :=
   match source j12' m1' b2 ofs2 with
                None => Undef
              | Some(b1,ofs1) => inject_memval j12'
                       (ZMap.get ofs1 (PMap.get b1 m1'.(Mem.mem_contents)))
   end.Definition ContentMap_EFF_Block_FUN b ofs : memval:=
  if plt b (Mem.nextblock m2)
  then ContentMap_EFF_ValidBlock_FUN b ofs
  else ContentMap_EFF_InvalidBlock_FUN b ofs.

Lemma CM_block_EFF_existsT: forall b, { M : ZMap.t memval | fst M = Undef /\ forall ofs, ZMap.get ofs M = ContentMap_EFF_Block_FUN b ofs}.