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4vmasklist-p

4vmasklist-p-basics

Basic theorems about 4vmasklist-p, generated by std::deflist.

Definitions and Theorems

Theorem: 4vmasklist-p-of-cons

(defthm 4vmasklist-p-of-cons
  (equal (4vmasklist-p (cons acl2::a x))
         (and (4vmask-p acl2::a)
              (4vmasklist-p x)))
  :rule-classes ((:rewrite)))

Theorem: 4vmasklist-p-of-cdr-when-4vmasklist-p

(defthm 4vmasklist-p-of-cdr-when-4vmasklist-p
  (implies (4vmasklist-p (double-rewrite x))
           (4vmasklist-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: 4vmasklist-p-when-not-consp

(defthm 4vmasklist-p-when-not-consp
  (implies (not (consp x))
           (equal (4vmasklist-p x) (not x)))
  :rule-classes ((:rewrite)))

Theorem: 4vmask-p-of-car-when-4vmasklist-p

(defthm 4vmask-p-of-car-when-4vmasklist-p
  (implies (4vmasklist-p x)
           (iff (4vmask-p (car x))
                (or (consp x) (4vmask-p nil))))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-4vmasklist-p-compound-recognizer

(defthm true-listp-when-4vmasklist-p-compound-recognizer
  (implies (4vmasklist-p x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: 4vmasklist-p-of-list-fix

(defthm 4vmasklist-p-of-list-fix
  (implies (4vmasklist-p x)
           (4vmasklist-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: 4vmasklist-p-of-rev

(defthm 4vmasklist-p-of-rev
  (equal (4vmasklist-p (rev x))
         (4vmasklist-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: 4vmasklist-p-of-repeat

(defthm 4vmasklist-p-of-repeat
  (iff (4vmasklist-p (repeat acl2::n x))
       (or (4vmask-p x) (zp acl2::n)))
  :rule-classes ((:rewrite)))