
theorem
  for V be homogeneous Abelian add-associative right_zeroed
  right_complementable vector-distributive scalar-distributive
  scalar-associative scalar-unital non empty RLSMetrStruct for r be
  Real for v be Element of V holds Norm (r * v) = |.r.| * Norm v
proof
  let V be homogeneous Abelian add-associative right_zeroed
  right_complementable vector-distributive scalar-distributive
  scalar-associative scalar-unital non empty RLSMetrStruct;
  let r be Real;
  let v be Element of V;
  thus Norm (r * v) = dist(r*(0.V),r * v) by RLVECT_1:10
    .= |.r.| * Norm (v) by Def5;
end;
