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;
