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

theorem
  X (/\) (Y (\) Z) = X (/\) Y (\) X (/\) Z
proof
A1: X (/\) Y c= X by Th15;
  X (/\) Y (\) X (/\) Z = ((X (/\) Y) (\) X) (\/) ((X (/\) Y) (\) Z) by Th69
    .= EmptyMS I (\/) ((X (/\) Y) (\) Z) by A1,Th52
    .= (X (/\) Y) (\) Z by Th22,Th43;
  hence thesis by Th62;
end;
