
theorem
  for V being RealNormSpace,
      x be Point of V,
      y,z be Point of DualSp V,
      a,b be Real holds
    x .|. (a*y + b*z) = a * x .|. y + b * x .|. z
proof
  let V be RealNormSpace,
      x be Point of V,
      y,z be Point of DualSp V,
      a,b be Real;
  thus x .|. (a*y + b*z) = x .|. (a*y) + x .|. (b*z) by DUALSP01:29
  .= a * x .|. y + x .|. (b*z) by DUALSP01:30
  .= a * x .|. y + b * x .|. z by DUALSP01:30;
end;
