reserve X for non empty set;

theorem Th6:
  for A being set, a,b being Element of EqRelLATT A holds a <= b iff a c= b
proof
  let A be set, a,b be Element of EqRelLATT A;
  set El = EqRelLatt A;
  reconsider a9 = a as Element of El;
  reconsider b9 = b as Element of El;
  thus a <= b implies a c= b
  proof
    assume a <= b;
    then a9% <= b9%;
    then a9 [= b9 by LATTICE3:7;
    hence thesis by Th5;
  end;
  thus a c= b implies a <= b
  proof
    assume a c= b;
    then a9 [= b9 by Th5;
    then a9% <= b9% by LATTICE3:7;
    hence thesis;
  end;
end;
