
theorem
  for T being TopStruct, x, y being Point of T, X, Y being Subset of T
  st X = {x} & Cl X c= Cl Y holds x in Cl Y
proof
  let T be TopStruct, x, y be Point of T, X, Y be Subset of T such that
A1: X = {x} and
A2: Cl X c= Cl Y;
  X c= Cl X by PRE_TOPC:18;
  then
A3: X c= Cl Y by A2;
  x in X by A1,TARSKI:def 1;
  hence thesis by A3;
end;
