reserve n for Element of NAT,
  a, r for Real,
  x for Point of TOP-REAL n;
reserve n for Element of NAT,
  r for non negative Real,
  s, t, x for Point of TOP-REAL n;
reserve n for non zero Element of NAT,
  s, t, o for Point of TOP-REAL n;

theorem
  for r being non negative Real, o being Point of TOP-REAL 2, f
being continuous Function of Tdisk(o,r), Tdisk(o,r) ex x being Point of Tdisk(o
  ,r) st f.x = x
proof
  let r be non negative Real, o be Point of TOP-REAL 2, f be
  continuous Function of Tdisk(o,r), Tdisk(o,r);
  f is with_fixpoint by Th14;
  then consider x being object such that
A1: x is_a_fixpoint_of f;
   reconsider x as set by TARSKI:1;
  take x;
  x in dom f by A1;
  hence x is Point of Tdisk(o,r);
  thus f.x = x by A1;
end;
