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 implies X (\) Y c= Z & X (\) Z c= Y
proof
  assume
A1: X c= Y (\/) Z;
  then X (\) Y c= Z (\/) Y (\) Y by Th53;
  then
A2: X (\) Y c= Z (\) Y by Th75;
  Z (\) Y c= Z by Th56;
  hence X (\) Y c= Z by A2,Th13;
  X (\) Z c= Y (\/) Z (\) Z by A1,Th53;
  then
A3: X (\) Z c= Y (\) Z by Th75;
  Y (\) Z c= Y by Th56;
  hence thesis by A3,Th13;
end;
