
theorem
  for V be translatible add-associative right_zeroed
  right_complementable non empty RLSMetrStruct for v,w be Element of V holds
  dist(v,w) = Norm (w - v)
proof
  let V be translatible add-associative right_zeroed right_complementable non
  empty RLSMetrStruct;
  let v,w be Element of V;
  thus dist(v,w) = dist(v + -v,w + -v) by Def6
    .= Norm (w - v) by RLVECT_1:5;
end;
