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
  X overlaps Y implies X meets Y
proof
  set i = the Element of I;
  assume X overlaps Y;
  then X.i meets Y.i;
  hence thesis;
end;
