reserve X,Y,Z,Z1,Z2,D for set,x,y for object;

theorem
  meet {X} = X
proof
A1: X c= meet {X}
  proof
    let y be object;
    assume y in X;
    then for Z st Z in {X} holds y in Z by TARSKI:def 1;
    hence thesis by Def1;
  end;
  X in {X} by TARSKI:def 1;
  then meet {X} c= X by Th3;
  hence thesis by A1;
end;
