reserve n for Element of NAT,
  a, r for Real,
  x for Point of TOP-REAL n;

theorem Th2:
  cl_Ball(x,0) = {x}
proof
  thus cl_Ball(x,0) c= {x}
  proof
    let a be object;
    assume
A1: a in cl_Ball(x,0);
    then reconsider a as Point of TOP-REAL n;
    |. a-x .| = 0 by A1,TOPREAL9:8;
    then a = x by TOPRNS_1:28;
    hence thesis by TARSKI:def 1;
  end;
  let a be object;
  assume a in {x};
  then
A2: a = x by TARSKI:def 1;
  |. x-x .| = 0 by TOPRNS_1:28;
  hence thesis by A2,TOPREAL9:8;
end;
