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;

theorem Th1:
  0 <= a & a <= b implies |.a.| <= |.b.|
proof
  assume that
A1: 0 <= a and
A2: a <= b;
  |.a.| = a by A1,ABSVALUE:def 1;
  hence thesis by A1,A2,ABSVALUE:def 1;
end;
