reserve
  x for object, X for set,
  i, n, m for Nat,
  r, s for Real,
  c, c1, c2, d for Complex,
  f, g for complex-valued Function,
  g1 for n-element complex-valued FinSequence,
  f1 for n-element real-valued FinSequence,
  T for non empty TopSpace,
  p for Element of TOP-REAL n;

theorem Th11:
  |. (n|->r) - (n|->s) .| = sqrt(n) * |.r-s.|
  proof
    thus |. (n|->r) - (n|->s) .| = sqrt Sum sqr (n|->(r-s)) by RVSUM_1:30
    .= sqrt Sum (n|->(r-s)^2) by RVSUM_1:56
    .= sqrt (n*(r-s)^2) by RVSUM_1:80
    .= sqrt n * sqrt((r-s)^2) by SQUARE_1:29
    .= sqrt n * |.r-s.| by COMPLEX1:72;
  end;
