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, t being Element of SCM+FSA-Data*-Loc, u
being FinSequence of INT, a being Element of SCM+FSA-Data-Loc holds SCM+FSA-Chg
  (s,t,u).a = s.a
proof
  let s be SCM+FSA-State, t be Element of SCM+FSA-Data*-Loc, u be FinSequence
  of INT, mk be Element of SCM+FSA-Data-Loc;
  (SCM*-VAL*SCM+FSA-OK).t = INT* & (SCM*-VAL*SCM+FSA-OK).mk = INT by Th5,Th6;
  then not mk in dom(t .--> u) by FUNCT_7:16,TARSKI:def 1;
  hence thesis by FUNCT_4:11;
end;
