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 Th1:
 ((SCM-VAL G)*SCM-OK).NAT = NAT
proof
A1: NAT in SCM-Memory by AMI_2:22;
   then NAT in dom SCM-OK by PARTFUN1:def 2;
   then
A2: ((SCM-VAL G)*SCM-OK).NAT = (SCM-VAL G).(SCM-OK.NAT) by FUNCT_1:13;
   ((SCM-VAL G)*SCM-OK).NAT = (SCM-VAL G).0 by A2,A1,AMI_2:def 4;
  hence thesis;
end;
