reserve x for object;
reserve D for set;
reserve p for PartialPredicate of D;
reserve D for non empty set;
reserve p,q,r for PartialPredicate of D;

theorem Th61:
  Bottom PartialPredConnectivesLatt(D) = PP_False(D)
  proof
    set L = PartialPredConnectivesLatt(D);
    reconsider f = PP_False(D) as Element of L by PARTFUN1:45;
    for a being Element of L holds f "/\" a = f & a "/\" f = f
    proof
      let a be Element of L;
      reconsider a1 = a as PartialPredicate of D by PARTFUN1:46;
      thus f"/\"a = PP_and(PP_False(D),a1) by Def11
      .= f by Th47;
      hence thesis;
    end;
    hence thesis by LATTICES:def 16;
  end;
