
(DEFPARAMETER |DirectProductCategory;CAT| 'NIL) 

(DECLAIM (NOTINLINE |DirectProductCategory;|)) 

(DEFPARAMETER |DirectProductCategory;AL| 'NIL) 

(DEFUN |DirectProductCategory| (|t#1| |t#2|)
  (LET (#1=#:G5 (#2=#:G6 (LIST |t#1| (|devaluate| |t#2|))))
    (COND ((SETQ #1# (|assoc| #2# |DirectProductCategory;AL|)) (CDR #1#))
          (T
           (SETQ |DirectProductCategory;AL|
                   (|cons5|
                    (CONS #2#
                          (SETQ #1# (APPLY #'|DirectProductCategory;| #2#)))
                    |DirectProductCategory;AL|))
           #1#)))) 

(DEFUN |DirectProductCategory;| (|t#1| |t#2|)
  (SPROG ((#1=#:G4 NIL))
         (PROG1
             (LETT #1#
                   (|subst_in_cat| '(|t#1| |t#2|) (LIST |t#1| |t#2|)
                                   (|subst_in_cat| '(#2=#:G2 #3=#:G3)
                                                   (LIST '(|Integer|)
                                                         '(|Vector| |t#2|))
                                                   (COND
                                                    (|DirectProductCategory;CAT|)
                                                    ('T
                                                     (LETT
                                                      |DirectProductCategory;CAT|
                                                      (|Join|
                                                       (|IndexedAggregate| '#2#
                                                                           '|t#2|)
                                                       (|CoercibleTo| '#3#)
                                                       (|AbelianProductCategory|
                                                        '|t#2|)
                                                       (|finiteAggregate|)
                                                       (|mkCategory|
                                                        '(((|directProduct|
                                                            (%
                                                             (|Vector| |t#2|)))
                                                           T)
                                                          ((|unitVector|
                                                            (%
                                                             (|PositiveInteger|)))
                                                           (AND
                                                            (|has| |t#2|
                                                                   (|Monoid|))
                                                            (|has| |t#2|
                                                                   (|AbelianMonoid|))))
                                                          ((|dot| (|t#2| % %))
                                                           (AND
                                                            (|has| |t#2|
                                                                   (|AbelianMonoid|))
                                                            (|has| |t#2|
                                                                   (|SemiRng|))))
                                                          ((* (% |t#2| %))
                                                           (|has| |t#2|
                                                                  (|SemiGroup|)))
                                                          ((* (% % |t#2|))
                                                           (|has| |t#2|
                                                                  (|SemiGroup|))))
                                                        '(((|FullyRetractableTo|
                                                            |t#2|)
                                                           (|has| |t#2|
                                                                  (|SetCategory|)))
                                                          ((|DifferentialExtension|
                                                            |t#2|)
                                                           (|has| |t#2|
                                                                  (|Ring|)))
                                                          ((|FullyLinearlyExplicitOver|
                                                            |t#2|)
                                                           (|has| |t#2|
                                                                  (|Ring|)))
                                                          ((|SemiRng|)
                                                           (|has| |t#2|
                                                                  (|SemiRng|)))
                                                          ((|BiModule| |t#2|
                                                                       |t#2|)
                                                           (|has| |t#2|
                                                                  (|SemiRng|)))
                                                          ((|Monoid|)
                                                           (|has| |t#2|
                                                                  (|Monoid|)))
                                                          ((|SemiGroup|)
                                                           (|has| |t#2|
                                                                  (|SemiGroup|)))
                                                          ((|Finite|)
                                                           (|has| |t#2|
                                                                  (|Finite|)))
                                                          ((|Algebra| |t#2|)
                                                           (|has| |t#2|
                                                                  (|CommutativeRing|)))
                                                          ((|CommutativeRing|)
                                                           (|has| |t#2|
                                                                  (|CommutativeRing|)))
                                                          ((|unitsKnown|)
                                                           (|has| |t#2|
                                                                  (|unitsKnown|)))
                                                          ((|OrderedSet|)
                                                           (|has| |t#2|
                                                                  (|OrderedSet|)))
                                                          ((|OrderedAbelianMonoid|)
                                                           (|has| |t#2|
                                                                  (|OrderedAbelianMonoid|)))
                                                          ((|OrderedAbelianMonoidSup|)
                                                           (|has| |t#2|
                                                                  (|OrderedAbelianMonoidSup|))))
                                                        NIL NIL))))))))
           (SETELT #1# 0 (LIST '|DirectProductCategory| |t#1| |t#2|))))) 
