reserve X for non empty set;

theorem Th8:
  for A being set, a,b being Element of EqRelLATT A holds a "/\" b = a /\ b
proof
  let A be set, a,b be Element of EqRelLATT A;
A1: now
    let x,y be Element of EqRelLatt A;
    reconsider e1 = x as Equivalence_Relation of A by MSUALG_5:21;
    reconsider e2 = y as Equivalence_Relation of A by MSUALG_5:21;
    thus x "/\" y = (the L_meet of EqRelLatt A).(e1,e2) by LATTICES:def 2
      .= x /\ y by MSUALG_5:def 2;
  end;
  reconsider y = b as Element of LattPOSet EqRelLatt A;
  reconsider x = a as Element of LattPOSet EqRelLatt A;
  reconsider x as Element of EqRelLatt A;
  reconsider y as Element of EqRelLatt A;
  %(x%) = x% & %(y%) = y%;
  hence a "/\" b = x "/\" y by Th7
    .= a /\ b by A1;
end;
