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
  for a, r being Real holds r >= 0 implies a in [.a-r,a+r.]
proof
  let a, r be Real;
  assume
A1: r >= 0;
  reconsider a, r as Real;
A2: a+0 <= a+r by A1,XREAL_1:7;
  reconsider amr=a-r, apr=a+r as Real;
  reconsider X = [.amr,apr.] as Subset of REAL;
A3: X = {b where b is Real : amr <= b & b <= apr} by RCOMP_1:def 1;
  a-r <= a-0 by A1,XREAL_1:13;
  hence thesis by A3,A2;
end;
