| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/PVS/orders/ (Beweissystem der NASA Version 6.0.9©) Datei vom 28.9.2014 mit Größe 1 kB |
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Quelle converse_zorn.pvs Sprache: PVS |
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% % The converse of Zorn's lemma: if every chain has a lower bound, then % the set has a minimal element. % % For PVS version 3.2. January 17, 2005 % --------------------------------------------------------------------- % Author: Jerry James (jamesj@acm.org), University of Kansas % % EXPORTS % ------- % prelude: orders[T], relations[T], sets[T] % orders: bounded_orders[T], chain[T,<=], converse_zorn[T,<=], % minmax_orders[T], relations_extra[T] % %------------------------------------------------------------------------- converse_zorn[T: TYPE, <=: (partial_order?[T])]: THEORY EXPORTING ALL WITH orders[T], relations[T], sets[T], bounded_orders[T], chain[T, <=], minmax_orders[T], relations_extra[T] BEGIN IMPORTING minmax_orders[T], chain[T, <=] IMPORTING relation_converse_props[T], zorn[T, converse(<=)] % Proof only converse_zorn: THEOREM (FORALL (ch: chain[T, <=]): bounded_below?[T](ch, <=)) => (EXISTS (t: T): minimal?[T](t, fullset[T], <=)) END converse_zorn ¤ Dauer der Verarbeitung: 0.11 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28