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
  PP_imp(PP_BottomPred(D),PP_True(D)) = PP_True(D)
  proof
    thus PP_imp(PP_BottomPred(D),PP_True(D))
     = PP_or(PP_BottomPred(D),PP_True(D)) by Th56
    .= PP_True(D) by Th57;
  end;
