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Named-lit-list-map

Named-lit-list-map-p

Signature
(named-lit-list-map-p x) → *

Definitions and Theorems

Function: named-lit-list-map-p

(defun named-lit-list-map-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'named-lit-list-map-p))
    (declare (ignorable __function__))
    (if (atom x)
        (eq x nil)
      (and (consp (car x))
           (symbolp (caar x))
           (lit-listp (cdar x))
           (named-lit-list-map-p (cdr x))))))

Theorem: named-lit-list-map-p-of-repeat

(defthm named-lit-list-map-p-of-repeat
  (iff (named-lit-list-map-p (acl2::repeat acl2::n x))
       (or (and (consp x)
                (symbolp (car x))
                (lit-listp (cdr x)))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: named-lit-list-map-p-of-butlast

(defthm named-lit-list-map-p-of-butlast
  (implies (named-lit-list-map-p (double-rewrite x))
           (named-lit-list-map-p (butlast x acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: named-lit-list-map-p-of-rev

(defthm named-lit-list-map-p-of-rev
  (equal (named-lit-list-map-p (acl2::rev x))
         (named-lit-list-map-p (acl2::list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: named-lit-list-map-p-of-append

(defthm named-lit-list-map-p-of-append
  (equal (named-lit-list-map-p (append acl2::a acl2::b))
         (and (named-lit-list-map-p (acl2::list-fix acl2::a))
              (named-lit-list-map-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: named-lit-list-map-p-of-list-fix

(defthm named-lit-list-map-p-of-list-fix
  (implies (named-lit-list-map-p x)
           (named-lit-list-map-p (acl2::list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-named-lit-list-map-p-compound-recognizer

(defthm true-listp-when-named-lit-list-map-p-compound-recognizer
  (implies (named-lit-list-map-p x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: named-lit-list-map-p-when-not-consp

(defthm named-lit-list-map-p-when-not-consp
  (implies (not (consp x))
           (equal (named-lit-list-map-p x)
                  (not x)))
  :rule-classes ((:rewrite)))

Theorem: named-lit-list-map-p-of-cdr-when-named-lit-list-map-p

(defthm named-lit-list-map-p-of-cdr-when-named-lit-list-map-p
  (implies (named-lit-list-map-p (double-rewrite x))
           (named-lit-list-map-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: named-lit-list-map-p-of-cons

(defthm named-lit-list-map-p-of-cons
  (equal (named-lit-list-map-p (cons acl2::a x))
         (and (and (consp acl2::a)
                   (symbolp (car acl2::a))
                   (lit-listp (cdr acl2::a)))
              (named-lit-list-map-p x)))
  :rule-classes ((:rewrite)))

Theorem: named-lit-list-map-p-of-remove-assoc

(defthm named-lit-list-map-p-of-remove-assoc
  (implies (named-lit-list-map-p x)
           (named-lit-list-map-p (remove-assoc-equal acl2::name x)))
  :rule-classes ((:rewrite)))

Theorem: named-lit-list-map-p-of-put-assoc

(defthm named-lit-list-map-p-of-put-assoc
 (implies
  (and (named-lit-list-map-p x))
  (iff
     (named-lit-list-map-p (put-assoc-equal acl2::name acl2::val x))
     (and (symbolp acl2::name)
          (lit-listp acl2::val))))
 :rule-classes ((:rewrite)))

Theorem: named-lit-list-map-p-of-fast-alist-clean

(defthm named-lit-list-map-p-of-fast-alist-clean
  (implies (named-lit-list-map-p x)
           (named-lit-list-map-p (fast-alist-clean x)))
  :rule-classes ((:rewrite)))

Theorem: named-lit-list-map-p-of-hons-shrink-alist

(defthm named-lit-list-map-p-of-hons-shrink-alist
  (implies (and (named-lit-list-map-p x)
                (named-lit-list-map-p acl2::y))
           (named-lit-list-map-p (hons-shrink-alist x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: named-lit-list-map-p-of-hons-acons

(defthm named-lit-list-map-p-of-hons-acons
  (equal (named-lit-list-map-p (hons-acons acl2::a acl2::n x))
         (and (symbolp acl2::a)
              (lit-listp acl2::n)
              (named-lit-list-map-p x)))
  :rule-classes ((:rewrite)))

Theorem: lit-listp-of-cdr-of-hons-assoc-equal-when-named-lit-list-map-p

(defthm
     lit-listp-of-cdr-of-hons-assoc-equal-when-named-lit-list-map-p
  (implies (named-lit-list-map-p x)
           (iff (lit-listp (cdr (hons-assoc-equal acl2::k x)))
                (or (hons-assoc-equal acl2::k x)
                    (lit-listp nil))))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-named-lit-list-map-p-rewrite

(defthm alistp-when-named-lit-list-map-p-rewrite
  (implies (named-lit-list-map-p x)
           (alistp x))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-named-lit-list-map-p

(defthm alistp-when-named-lit-list-map-p
  (implies (named-lit-list-map-p x)
           (alistp x))
  :rule-classes :tau-system)

Theorem: lit-listp-of-cdar-when-named-lit-list-map-p

(defthm lit-listp-of-cdar-when-named-lit-list-map-p
  (implies (named-lit-list-map-p x)
           (iff (lit-listp (cdar x))
                (or (consp x) (lit-listp nil))))
  :rule-classes ((:rewrite)))

Theorem: symbolp-of-caar-when-named-lit-list-map-p

(defthm symbolp-of-caar-when-named-lit-list-map-p
  (implies (named-lit-list-map-p x)
           (iff (symbolp (caar x))
                (or (consp x) (symbolp nil))))
  :rule-classes ((:rewrite)))