theorem
  for s being SCM+FSA-State, u being Nat, p being Element of
  SCM+FSA-Data*-Loc holds SCM+FSA-Chg(s,u).p = s.p
proof
  let s be SCM+FSA-State, u be Nat,
      mk be Element of SCM+FSA-Data*-Loc;
A2: SCM+FSA-OK.NAT = 0 by Lm4;
  SCM+FSA-OK.mk = 2 by Lm6;
  then NAT <> mk by A2;
  then not mk in dom(NAT .--> u) by TARSKI:def 1;
  hence thesis by FUNCT_4:11;
end;
