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

theorem Th10:
  x in X & x in Y implies X overlaps Y
proof
  assume
A1: x in X & x in Y;
  let i be object;
  assume i in I;
  then x.i in X.i & x.i in Y.i by A1;
  hence thesis by XBOOLE_0:3;
end;
