reserve i,j,e,u for object;
reserve I for set; 
reserve x,X,Y,Z,V for ManySortedSet of I;

theorem
  (X (/\) Y) (\/) (Y (/\) Z) (\/) (Z (/\) X)
    = (X (\/) Y) (/\) (Y (\/) Z) (/\) (Z (\/) X)
proof
  thus X (/\) Y (\/) Y (/\) Z (\/) Z (/\) X
      = (X (/\) Y (\/) Y (/\) Z (\/) Z) (/\) (X (/\) Y (\/) Y (/\) Z (\/) X)
         by Th33
    .= (X (/\) Y (\/) (Y (/\) Z (\/) Z)) (/\) (X (/\) Y (\/) Y (/\) Z (\/) X)
         by Th28
    .= (X (/\) Y (\/) Z) (/\) (X (/\) Y (\/) Y (/\) Z (\/) X) by Th31
    .= (X (/\) Y (\/) Z) (/\) (X (/\) Y (\/) X (\/) Y (/\) Z) by Th28
    .= (X (/\) Y (\/) Z) (/\) (X (\/) Y (/\) Z) by Th31
    .= (X (\/) Z) (/\) (Y (\/) Z) (/\) (X (\/) Y (/\) Z) by Th33
    .= (X (\/) Z) (/\) (Y (\/) Z) (/\) ((X (\/) Y) (/\) (X (\/) Z)) by Th33
    .= (X (\/) Y) (/\) ((Y (\/) Z) (/\) (X (\/) Z) (/\) (X (\/) Z)) by Th29
    .= (X (\/) Y) (/\) ((Y (\/) Z) (/\) ((X (\/) Z) (/\) (X (\/) Z))) by Th29
    .= (X (\/) Y) (/\) (Y (\/) Z) (/\) (Z (\/) X) by Th29;
end;
