%============================================================================%
% LIBRARY:     wellorder                                                     %
%                                                                            %
% DESCRIPTION: (1) Versions of the Axiom of Choice                           %
%              (2) Theorems about wosets, including recursion theorem        %
%                                                                            %
% AUTHOR:      John Harrison                                                 %
%              University of Cambridge Computer Laboratory                   %
%              New Museums Site                                              %
%              Pembroke Street                                               %
%              Cambridge CB2 3QG                                             %
%              England.                                                      %
%                                                                            %
%              jrh@cl.cam.ac.uk                                              %
%                                                                            %
% DATE:        30th May 1992    [Original version written]                   %
% REVISED:     31st Mar 1993    [Recursion theorem added]                    %
%                                                                            %
% DETAILS:     The versions of the axiom of choice proved bere are:          %
%                                                                            %
%              1. Kuratowski's Lemma:                                        %
%                 Every chain is a poset can be extended to a maximal        %
%                 chain.                                                     %
%                                                                            %
%              2. Hausdorff Maximum Principle:                               %
%                 Every poset has a maximal chain.                           %
%                                                                            %
%              3. Zorn's Lemma:                                              %
%                 A poset where every chain has an upper bound, has a        %
%                 maximal element.                                           %
%                                                                            %
%              4. Cantor-Zermelo well-ordering theorem:                      %
%                 Every set can be wellordered.                              %
%                                                                            %
%              Proofs follow quite closely those in "R.R. Stoll - Set        %
%              Theory and Logic - Dover 1979"                                %
%                                                                            %
%              The recursion theorem justifies arbitrary recursive           %
%              definitions:                                                  %
%                                                                            %
%                ?!f. f a = h f a                                            %
%                                                                            %
%              provided one can prove that for some wellfounded              %
%              "measure" function, the value of |h f a| depends              %
%              only on the values of |f| at values of lower measure          %
%              than |a|.                                                     %
%============================================================================%

This library is intended to supersede an earlier library of the same name
written by Ton Kalker, which stopped working in HOL version 1.12. Its format
and the structure of the proofs is somewhat different, providing three maximal
principles: Kuratowski's Lemma, Hausdorff's Maximal Principle and Zorn's Lemma,
en route to the Well-Ordering Theorem. The revised version also includes a
theorem justifying transfinite recursion.

For full documentation, see "Manual/wellorder.dvi".
