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 holds SCM+FSA-Chg(s,
  u).NAT = u
proof
  let s be SCM+FSA-State, u be Nat;
  NAT in dom(NAT .--> u) by TARSKI:def 1;
  hence SCM+FSA-Chg(s,u).NAT = (NAT .--> u).NAT by FUNCT_4:13
    .= u by FUNCOP_1:72;
end;
