reserve I for non empty set;
reserve M for ManySortedSet of I;
reserve Y,x,y,y1,i,j for set;
reserve k for Element of NAT;
reserve p for FinSequence;
reserve S for non void non empty ManySortedSign;
reserve A for non-empty MSAlgebra over S;

theorem
  Bottom EqRelLatt Y = id Y
proof
  reconsider K = id Y as Element of EqRelLatt Y by MSUALG_5:21;
  now
    let a be Element of EqRelLatt Y;
    reconsider a9 = a as Equivalence_Relation of Y by MSUALG_5:21;
    thus K "/\" a = (the L_meet of EqRelLatt Y).(K,a) by LATTICES:def 2
      .= id Y /\ a9 by MSUALG_5:def 2
      .= K by EQREL_1:10;
    hence a "/\" K = K;
  end;
  hence thesis by LATTICES:def 16;
end;
