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

theorem Th127:
  X (/\) Y = EmptyMS I implies X does not overlap Y
proof
  assume
A1: X (/\) Y = EmptyMS I;
  assume X overlaps Y;
  then consider x such that
A2: x in X & x in Y by Th11;
  x in X (/\) Y by A2,Th8;
  hence contradiction by A1,Th124;
end;
