reserve x,y,z for set,
  k for Nat;
reserve J,J1,K for Element of Segm 13,
  a for Nat,
  b,b1,b2,c,c1,c2 for Element of SCM+FSA-Data-Loc,
  f,f1,f2 for Element of SCM+FSA-Data*-Loc;

theorem
  for s being SCM+FSA-State, u being Nat, mk being Element of
  SCM+FSA-Data-Loc holds SCM+FSA-Chg(s,u).mk = s.mk
proof
  let s be SCM+FSA-State, u be Nat, mk be Element of
  SCM+FSA-Data-Loc;
  (SCM*-VAL*SCM+FSA-OK).mk = INT & {NAT} = dom(NAT .--> u) by Th5;
  then not mk in dom(NAT .--> u) by Th4,NUMBERS:7,TARSKI:def 1;
  hence thesis by FUNCT_4:11;
end;
