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 Th4:
  pi(product((SCM-VAL G)*SCM-OK),NAT) = NAT
proof
   NAT in dom((SCM-VAL G)*SCM-OK) by Lm1,AMI_2:22;
  hence pi(product((SCM-VAL G)*SCM-OK),NAT)
     = ((SCM-VAL G)*SCM-OK).NAT by CARD_3:12
    .= NAT by Th1;
end;
