reserve i, j, k for Element of NAT,
  I for Element of Segm 8,
  i1, i2 for Element of NAT,
  d1, d2, d3, d4 for Element of SCM-Data-Loc,
  S for non empty 1-sorted;
reserve G for non empty 1-sorted;

theorem Th2:
  for i being Element of SCM-Memory st i in SCM-Data-Loc
   holds ((SCM-VAL G)*SCM-OK).i = the carrier of G
proof
  let i be Element of SCM-Memory;
   i in SCM-Memory;
   then i in dom SCM-OK by PARTFUN1:def 2;
   then
A1: ((SCM-VAL G)*SCM-OK).i = (SCM-VAL G).(SCM-OK.i) by FUNCT_1:13;
  assume i in SCM-Data-Loc;
   then ((SCM-VAL G)*SCM-OK).i = (SCM-VAL G).1 by A1,AMI_2:def 4;
  hence thesis;
end;
