
(DEFPARAMETER |Poset;CAT| 'NIL) 

(DECLAIM (NOTINLINE |Poset;|)) 

(DEFPARAMETER |Poset;AL| 'NIL) 

(DEFUN |Poset| (|t#1|)
  (LET (#1=#:G723 (#2=#:G724 (|devaluate| |t#1|)))
    (COND ((SETQ #1# (|assoc| #2# |Poset;AL|)) (CDR #1#))
          (T
           (SETQ |Poset;AL|
                   (|cons5| (CONS #2# (SETQ #1# (|Poset;| #2#))) |Poset;AL|))
           #1#)))) 

(DEFUN |Poset;| (|t#1|)
  (SPROG ((#1=#:G722 NIL))
         (PROG1
             (LETT #1#
                   (|sublisV| (PAIR '(|t#1|) (LIST |t#1|))
                              (COND (|Poset;CAT|)
                                    ('T
                                     (LETT |Poset;CAT|
                                           (|Join| (|Preorder| '|t#1|)
                                                   (|mkCategory|
                                                    '(((|finitePoset|
                                                        ($ (|List| |t#1|)
                                                         (|List|
                                                          (|List|
                                                           (|Boolean|)))))
                                                       T)
                                                      ((|finitePoset|
                                                        ($ (|List| |t#1|)
                                                         (|Mapping| (|Boolean|)
                                                                    |t#1|
                                                                    |t#1|)))
                                                       T)
                                                      ((|getVert|
                                                        ((|List| |t#1|) $))
                                                       T)
                                                      ((|getArr|
                                                        ((|List|
                                                          (|List| (|Boolean|)))
                                                         $))
                                                       T)
                                                      ((|setVert|
                                                        ((|Void|) $
                                                         (|List| |t#1|)))
                                                       T)
                                                      ((|setArr|
                                                        ((|Void|) $
                                                         (|List|
                                                          (|List|
                                                           (|Boolean|)))))
                                                       T)
                                                      ((|addObject!|
                                                        ($ $ |t#1|))
                                                       T)
                                                      ((|addArrow!|
                                                        ($ $
                                                         (|NonNegativeInteger|)
                                                         (|NonNegativeInteger|)))
                                                       T)
                                                      ((|opposite| ($ $)) T)
                                                      ((|powerSetStructure|
                                                        ($ |t#1|))
                                                       T)
                                                      ((|implies|
                                                        ((|Boolean|) $
                                                         (|NonNegativeInteger|)
                                                         (|NonNegativeInteger|)))
                                                       T)
                                                      ((|meetIfCan|
                                                        ((|Union|
                                                          (|NonNegativeInteger|)
                                                          "failed")
                                                         $
                                                         (|NonNegativeInteger|)
                                                         (|NonNegativeInteger|)))
                                                       T)
                                                      ((|joinIfCan|
                                                        ((|Union|
                                                          (|NonNegativeInteger|)
                                                          "failed")
                                                         $
                                                         (|NonNegativeInteger|)
                                                         (|NonNegativeInteger|)))
                                                       T)
                                                      ((|meetIfCan|
                                                        ((|Union|
                                                          (|NonNegativeInteger|)
                                                          "failed")
                                                         $
                                                         (|List|
                                                          (|NonNegativeInteger|))))
                                                       T)
                                                      ((|joinIfCan|
                                                        ((|Union|
                                                          (|NonNegativeInteger|)
                                                          "failed")
                                                         $
                                                         (|List|
                                                          (|NonNegativeInteger|))))
                                                       T)
                                                      ((|glb|
                                                        ((|Union|
                                                          (|NonNegativeInteger|)
                                                          "failed")
                                                         $
                                                         (|List|
                                                          (|NonNegativeInteger|))))
                                                       T)
                                                      ((|lub|
                                                        ((|Union|
                                                          (|NonNegativeInteger|)
                                                          "failed")
                                                         $
                                                         (|List|
                                                          (|NonNegativeInteger|))))
                                                       T)
                                                      ((|upperSet| ($ $)) T)
                                                      ((|lowerSet| ($ $)) T)
                                                      ((|indexToObject|
                                                        (|t#1| $
                                                         (|NonNegativeInteger|)))
                                                       T)
                                                      ((|objectToIndex|
                                                        ((|NonNegativeInteger|)
                                                         $ |t#1|))
                                                       T)
                                                      ((|completeReflexivity|
                                                        ($ $))
                                                       T)
                                                      ((|completeTransitivity|
                                                        ($ $))
                                                       T)
                                                      ((|isAntisymmetric?|
                                                        ((|Boolean|) $))
                                                       T)
                                                      ((|isChain?|
                                                        ((|Boolean|) $))
                                                       T)
                                                      ((|isAntiChain?|
                                                        ((|Boolean|) $))
                                                       T)
                                                      ((|moebius|
                                                        ((|IncidenceAlgebra|
                                                          (|Integer|) |t#1|)
                                                         $))
                                                       T)
                                                      ((|zetaMatrix|
                                                        ((|IncidenceAlgebra|
                                                          (|Integer|) |t#1|)
                                                         $))
                                                       T)
                                                      ((|coverMatrix|
                                                        ((|IncidenceAlgebra|
                                                          (|Integer|) |t#1|)
                                                         $))
                                                       T))
                                                    NIL NIL NIL)))))))
           (SETELT #1# 0 (LIST '|Poset| |t#1|))))) 
