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 Th56:
  for D being set holds PP_not(PP_BottomPred(D)) = PP_BottomPred(D)
  proof
    let D be set;
    thus dom PP_not(PP_BottomPred(D)) = dom PP_BottomPred(D) by Def2;
    hence thesis;
  end;
