		Search-engine friendly clone of the ACL2 documentation.

Truthmap

Truthmap-p

Recognizer for truthmap.

Signature
(truthmap-p x) → *

Definitions and Theorems

Function: truthmap-p

(defun truthmap-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'truthmap-p))
    (declare (ignorable __function__))
    (if (atom x)
        t
      (and (consp (car x))
           (truth::truth4-p (caar x))
           (lit-listp (cdar x))
           (truthmap-p (cdr x))))))

Theorem: truthmap-p-of-repeat

(defthm truthmap-p-of-repeat
  (iff (truthmap-p (acl2::repeat acl2::n x))
       (or (and (consp x)
                (truth::truth4-p (car x))
                (lit-listp (cdr x)))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: truthmap-p-of-butlast

(defthm truthmap-p-of-butlast
  (implies (truthmap-p (double-rewrite x))
           (truthmap-p (butlast x acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: truthmap-p-of-rev

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

Theorem: truthmap-p-of-list-fix

(defthm truthmap-p-of-list-fix
  (equal (truthmap-p (acl2::list-fix x))
         (truthmap-p x))
  :rule-classes ((:rewrite)))

Theorem: truthmap-p-of-append

(defthm truthmap-p-of-append
  (equal (truthmap-p (append acl2::a acl2::b))
         (and (truthmap-p acl2::a)
              (truthmap-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: truthmap-p-when-not-consp

(defthm truthmap-p-when-not-consp
  (implies (not (consp x)) (truthmap-p x))
  :rule-classes ((:rewrite)))

Theorem: truthmap-p-of-cdr-when-truthmap-p

(defthm truthmap-p-of-cdr-when-truthmap-p
  (implies (truthmap-p (double-rewrite x))
           (truthmap-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: truthmap-p-of-cons

(defthm truthmap-p-of-cons
  (equal (truthmap-p (cons acl2::a x))
         (and (and (consp acl2::a)
                   (truth::truth4-p (car acl2::a))
                   (lit-listp (cdr acl2::a)))
              (truthmap-p x)))
  :rule-classes ((:rewrite)))

Theorem: truthmap-p-of-fast-alist-clean

(defthm truthmap-p-of-fast-alist-clean
  (implies (truthmap-p x)
           (truthmap-p (fast-alist-clean x)))
  :rule-classes ((:rewrite)))

Theorem: truthmap-p-of-hons-shrink-alist

(defthm truthmap-p-of-hons-shrink-alist
  (implies (and (truthmap-p x)
                (truthmap-p acl2::y))
           (truthmap-p (hons-shrink-alist x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: truthmap-p-of-hons-acons

(defthm truthmap-p-of-hons-acons
  (equal (truthmap-p (hons-acons acl2::a acl2::n x))
         (and (truth::truth4-p acl2::a)
              (lit-listp acl2::n)
              (truthmap-p x)))
  :rule-classes ((:rewrite)))

Theorem: lit-listp-of-cdr-of-hons-assoc-equal-when-truthmap-p

(defthm lit-listp-of-cdr-of-hons-assoc-equal-when-truthmap-p
  (implies (truthmap-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: lit-listp-of-cdar-when-truthmap-p

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

Theorem: truth4-p-of-caar-when-truthmap-p

(defthm truth4-p-of-caar-when-truthmap-p
  (implies (truthmap-p x)
           (iff (truth::truth4-p (caar x))
                (or (consp x) (truth::truth4-p nil))))
  :rule-classes ((:rewrite)))