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4vs-ite*-list-dumb

(4vs-ite*-list-dumb c as bs) produces a list of sexprs, basically (4V-ITE* C Ai Bi) for the corresponding elements of AS and BS.

Definitions and Theorems

Function: 4vs-ite*-list-dumb

(defun 4vs-ite*-list-dumb (c as bs)
  (declare (xargs :guard (equal (len as) (len bs))))
  (if (atom as)
      nil
    (cons (4vs-ite*-dumb c (car as) (car bs))
          (4vs-ite*-list-dumb c (cdr as)
                              (cdr bs)))))

Theorem: 4vs-ite*-list-dumb-when-atom

(defthm 4vs-ite*-list-dumb-when-atom
  (implies (atom as)
           (equal (4vs-ite*-list-dumb c as bs)
                  nil)))

Theorem: 4vs-ite*-list-dumb-of-cons

(defthm 4vs-ite*-list-dumb-of-cons
  (equal (4vs-ite*-list-dumb c (cons a as)
                             (cons b bs))
         (cons (4vs-ite*-dumb c a b)
               (4vs-ite*-list-dumb c as bs))))

Theorem: consp-of-4vs-ite*-list-dumb

(defthm consp-of-4vs-ite*-list-dumb
  (equal (consp (4vs-ite*-list-dumb c as bs))
         (consp as)))

Theorem: len-of-4vs-ite*-list-dumb

(defthm len-of-4vs-ite*-list-dumb
  (equal (len (4vs-ite*-list-dumb c as bs))
         (len as)))

Theorem: car-of-4vs-ite*-list-dumb

(defthm car-of-4vs-ite*-list-dumb
  (equal (car (4vs-ite*-list-dumb c as bs))
         (if (consp as)
             (4vs-ite*-dumb c (car as) (car bs))
           nil)))

Theorem: cdr-of-4vs-ite*-list-dumb

(defthm cdr-of-4vs-ite*-list-dumb
  (equal (cdr (4vs-ite*-list-dumb c as bs))
         (4vs-ite*-list-dumb c (cdr as)
                             (cdr bs))))

Theorem: 4v-sexpr-vars-list-of-4vs-ite*-list-dumb

(defthm 4v-sexpr-vars-list-of-4vs-ite*-list-dumb
 (implies
  (equal (len a) (len b))
  (set-equiv (4v-sexpr-vars-list (4vs-ite*-list-dumb c a b))
             (if (consp a)
                 (hons-alphorder-merge
                      (4v-sexpr-vars c)
                      (hons-alphorder-merge (4v-sexpr-vars-list a)
                                            (4v-sexpr-vars-list b)))
               nil))))