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 Th60:
  for r being non negative Real
  for n being non zero Nat, p being Point of Tcircle(0.TOP-REAL n,r)
  holds -p is Point of Tcircle(0.TOP-REAL n,r)
  proof
    let r be non negative Real;
    let n be non zero Nat;
    let p be Point of Tcircle(0.TOP-REAL n,r);
    reconsider p1 = p as Point of TOP-REAL n by PRE_TOPC:25;
 n in NAT by ORDINAL1:def 12;
    then
A1: the carrier of Tcircle(0.TOP-REAL n,r) = Sphere(0.TOP-REAL n,r)
    by TOPREALB:9;
    |. (-p1) - 0.TOP-REAL n .| = |. -p1 .|
    .= |. p1 .| by EUCLID:71
    .= |. p1 - 0.TOP-REAL n .|
    .= r by A1,TOPREAL9:9;
    hence thesis by A1,TOPREAL9:9;
  end;
