reserve x,y,z for set;
reserve I,J,K for Element of Segm 9,
  i,a,a1,a2 for Nat,
  b,b1,b2,c,c1 for Element of SCM-Data-Loc;

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