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 implies X (\/) Z c= Y (\/) Z
proof
  assume
A1: X c= Y;
A2: Z c= Y (\/) Z by Th14;
  Y c= Y (\/) Z by Th14;
  then X c= Y (\/) Z by A1,Th13;
  hence X (\/) Z c= Y (\/) Z by A2,Th16;
end;
