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• Namelist-p

Namelist-p-basics

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

Definitions and Theorems

Theorem: namelist-p-of-cons

(defthm namelist-p-of-cons
  (equal (namelist-p (cons acl2::a x))
         (and (name-p acl2::a) (namelist-p x)))
  :rule-classes ((:rewrite)))

Theorem: namelist-p-of-cdr-when-namelist-p

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

Theorem: namelist-p-when-not-consp

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

Theorem: name-p-of-car-when-namelist-p

(defthm name-p-of-car-when-namelist-p
  (implies (namelist-p x)
           (iff (name-p (car x))
                (or (consp x) (name-p nil))))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-namelist-p-compound-recognizer

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

Theorem: namelist-p-of-list-fix

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

Theorem: namelist-p-of-rev

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

Theorem: namelist-p-of-repeat

(defthm namelist-p-of-repeat
  (iff (namelist-p (repeat acl2::n x))
       (or (name-p x) (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: namelist-p-of-append

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

Theorem: namelist-p-of-take

(defthm namelist-p-of-take
  (implies (namelist-p (double-rewrite x))
           (iff (namelist-p (take acl2::n x))
                (or (name-p nil)
                    (<= (nfix acl2::n) (len x)))))
  :rule-classes ((:rewrite)))

Theorem: namelist-p-of-butlast

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