
theorem Th18:
  for K be left_unital non empty doubleLoopStr for V be non
  empty ModuleStr over K for f be Functional of V holds (1.K)*f = f
proof
  let K be left_unital non empty doubleLoopStr;
  let V be non empty ModuleStr over K;
  let f be Functional of V;
  now
    let x be Element of V;
    thus ((1.K)*f).x = (1.K)*f.x by Def6
      .= f.x;
  end;
  hence thesis by FUNCT_2:63;
end;
