
theorem Th6:
  for V being RealNormSpace,
      x be Point of V,
      y be Point of DualSp V,
      a be Real holds
    (a*x) .|. y = a* x .|. y
proof
  let V be RealNormSpace,
      x be Point of V,
      y be Point of DualSp V,
      a be Real;
  reconsider y1= y as linear-Functional of V by DUALSP01:def 10;
  thus (a*x) .|. y =y1.(a*x)
  .= a*x .|. y by HAHNBAN:def 3;
end;
