reserve n for Element of NAT,
  i for Integer,
  a, b, r for Real,
  x for Point of TOP-REAL n;

theorem Th6:
  for f being PartFunc of REAL,REAL st dom f = REAL holds R^1|(R^1 dom f) = R^1
proof
  let f be PartFunc of REAL,REAL;
  assume dom f = REAL;
  then [#]R^1 = R^1(dom f) by TOPMETR:17;
  hence thesis by PRE_TOPC:def 5;
end;
