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
  for s being SCM-State of G, u being natural Number holds SCM-Chg(s,u).NAT = u
proof
  let s be SCM-State of G, u be natural Number;
  NAT in dom(NAT .--> u) by TARSKI:def 1;
  hence SCM-Chg(s,u).NAT = (NAT .--> u).NAT by FUNCT_4:13
    .= u by FUNCOP_1:72;
end;
