theorem
  for s being SCM-State, u being natural Number,
  mk being Element of SCM-Data-Loc holds SCM-Chg(s,u).mk = s.mk
proof
  let s be SCM-State, u be natural Number, mk be Element of SCM-Data-Loc;
  (SCM-VAL*SCM-OK).NAT = NAT & (SCM-VAL*SCM-OK).mk = INT by Th1,Th2;
  then not mk in dom(NAT .--> u) by NUMBERS:7,TARSKI:def 1;
  hence thesis by FUNCT_4:11;
end;
