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 Th5:
  for a being Element of SCM-Data-Loc
   holds pi(product((SCM-VAL G)*SCM-OK),a) = the carrier of G
proof
  let a be Element of SCM-Data-Loc;
   a in SCM-Memory;
   then a in dom((SCM-VAL G)*SCM-OK) by Lm1;
  hence pi(product((SCM-VAL G)*SCM-OK),a)
     = ((SCM-VAL G)*SCM-OK).a by CARD_3:12
    .= the carrier of G by Th2;
end;
