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 iff Y c= X & Z c= X & for V st Y c= V & Z c= V holds X c= V
proof
  thus X = Y (\/) Z implies Y c= X & Z c= X & for V st Y c= V & Z c= V holds X
  c= V by Th14,Th16;
  assume that
A1: Y c= X & Z c= X and
A2: Y c= V & Z c= V implies X c= V;
  Y c= Y (\/) Z & Z c= Y (\/) Z by Th14;
  then
A3: X c= Y (\/) Z by A2;
   Y (\/) Z c= X by A1,Th16;
 hence thesis by A3,Lm1;
end;
