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

theorem Th31:
  X (\/) (X (/\) Y) = X
proof
  X (/\) Y c= X by Th15;
  then
A1: X (\/) (X (/\) Y) c= X by Th16;
 X c= X (\/) (X (/\) Y) by Th14;
  hence X (\/) (X (/\) Y) = X by A1,Lm1;
end;
