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

theorem Th33:
  X (\/) Y (/\) Z = (X (\/) Y) (/\) (X (\/) Z)
proof
  thus X (\/) Y (/\) Z = X (\/) X (/\) Z (\/) Y (/\) Z by Th31
    .= X (\/) (X (/\) Z (\/) Y (/\) Z) by Th28
    .= X (\/) (X (\/) Y) (/\) Z by Th32
    .= (X (\/) Y) (/\) X (\/) (X (\/) Y) (/\) Z by Th30
    .= (X (\/) Y) (/\) (X (\/) Z) by Th32;
end;
