reserve X,Y for set, x,y,z for object, i,j,n for natural number;

theorem
  for U1,U2 being Universal_Algebra st the UAStr of U1 = the UAStr of U2
  for S1 being Subset of U1, S2 being Subset of U2 st S1 = S2
  for o1 being operation of U1, o2 being operation of U2 st o1 = o2
  holds S1 is_closed_on o1 implies S2 is_closed_on o2;
