reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;

theorem Th13:
  varcl ((varcl X) /\ (varcl Y)) = (varcl X) /\ (varcl Y)
proof
  set A = (varcl X) /\ (varcl Y);
  now
    thus A c= A;
    let x,y;
    assume
A1: [x,y] in A;
    then
A2: [x,y] in varcl X by XBOOLE_0:def 4;
A3: [x,y] in varcl Y by A1,XBOOLE_0:def 4;
A4: x c= varcl X by A2,Def1;
    x c= varcl Y by A3,Def1;
    hence x c= A by A4,XBOOLE_1:19;
  end;
  hence varcl ((varcl X) /\ (varcl Y)) c= (varcl X) /\ (varcl Y) by Def1;
  thus thesis by Def1;
end;
