reserve X for non empty TopSpace;
reserve Y for non empty TopStruct;
reserve x for Point of Y;
reserve Y for non empty TopStruct;
reserve X for non empty TopSpace;
reserve x,y for Point of X;
reserve A, B for Subset of X;
reserve P, Q for Subset of X;

theorem Th60:
  P is closed implies MaxADSet(P) = P
proof
  assume P is closed;
  then
A1: Cl P = P by PRE_TOPC:22;
A2: P c= MaxADSet(P) by Th32;
  MaxADSet(P) c= Cl P by Th59;
  hence thesis by A1,A2;
end;
