
theorem Th6:
  for X be non empty set, Y be ComplexNormSpace, f be Function of X
  ,the carrier of Y st (for x be Element of X holds f.x=0.Y) holds f is bounded
proof
  let X be non empty set;
  let Y be ComplexNormSpace;
  let f be Function of X,the carrier of Y such that
A1: for x be Element of X holds f.x=0.Y;
A2: now
    let x be Element of X;
    thus ||. f.x .|| = ||. 0.Y .|| by A1
      .=0;
  end;
  take 0;
  thus thesis by A2;
end;
