reserve a, b for Real,
  r for Real,
  rr for Real,
  i, j, n for Nat,
  M for non empty MetrSpace,
  p, q, s for Point of TOP-REAL 2,
  e for Point of Euclid 2,
  w for Point of Euclid n,
  z for Point of M,
  A, B for Subset of TOP-REAL n,
  P for Subset of TOP-REAL 2,
  D for non empty Subset of TOP-REAL 2;
reserve a, b for Real;
reserve a, b for Real;

theorem
 |.|[0,a]|.| = |.a.| & |.|[a,0]|.| = |.a.|
proof
  reconsider aa = a as Real;
  reconsider a2 = aa^2, z2 = 0^2 as Real;
  |.<*0,aa*>.| = sqrt Sum <*z2,a2*> by Th10
    .= sqrt (0+a^2) by RVSUM_1:77
    .= |.a.| by COMPLEX1:72;
  hence |.|[0,a]|.| = |.a.|;
  |.<*aa,0 *>.| = sqrt Sum <*a2,z2 *> by Th10
    .= sqrt (a^2+0) by RVSUM_1:77
    .= |.a.| by COMPLEX1:72;
  hence thesis;
end;
