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 X c= Y & X c= Z & for V st V c= Y & V c= Z holds V c= X
proof
  thus X = Y (/\) Z implies X c= Y & X c= Z & for V st V c= Y & V c= Z holds V
  c= X by Th15,Th17;
  assume that
A1: X c= Y & X c= Z and
A2: V c= Y & V c= Z implies V c= X;
A3:  X c= Y (/\) Z by A1,Th17;
  Y (/\) Z c= Y & Y (/\) Z c= Z implies Y (/\) Z c= X by A2;
  hence thesis by A3,Lm1,Th15;
end;
