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

theorem
  X c= Y & Z c= V implies X (/\) Z c= Y (/\) V
proof
  assume that
A1: X c= Y and
A2: Z c= V;
  X (/\) Z c= Z by Th15;
  then
A3: X (/\) Z c= V by A2,Th13;
  X (/\) Z c= X by Th15;
  then X (/\) Z c= Y by A1,Th13;
  hence thesis by A3,Th17;
end;
