reserve r, s, t for Real;
reserve seq for Real_Sequence,
  X, Y for Subset of REAL;
reserve r3, r1, q3, p3 for Real;

theorem Th57:
  for Y being closed Subset of REAL st X c= Y holds Cl X c= Y
proof
  let Y be closed Subset of REAL;
  set ClX = { A where A is Subset of REAL : X c= A & A is closed };
  assume X c= Y;
  then Y in ClX;
  hence thesis by SETFAM_1:3;
end;
