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

theorem Th19:
  X c= Y implies X (/\) Z c= Y (/\) Z
proof
  assume
A1: X c= Y;
A2: X (/\) Z c= Z by Th15;
  X (/\) Z c= X by Th15;
  then X (/\) Z c= Y by A1,Th13;
  hence X (/\) Z c= Y (/\) Z by A2,Th17;
end;
