		Search-engine friendly clone of the ACL2 documentation.

Name-listp

Name-listp-basics

Basic theorems about name-listp, generated by std::deflist.

Definitions and Theorems

Theorem: name-listp-of-cons

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

Theorem: name-listp-of-cdr-when-name-listp

(defthm name-listp-of-cdr-when-name-listp
  (implies (name-listp (double-rewrite acl2::x))
           (name-listp (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: name-listp-when-not-consp

(defthm name-listp-when-not-consp
  (implies (not (consp acl2::x))
           (equal (name-listp acl2::x)
                  (not acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: namep-of-car-when-name-listp

(defthm namep-of-car-when-name-listp
  (implies (name-listp acl2::x)
           (iff (namep (car acl2::x))
                (consp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-name-listp-compound-recognizer

(defthm true-listp-when-name-listp-compound-recognizer
  (implies (name-listp acl2::x)
           (true-listp acl2::x))
  :rule-classes :compound-recognizer)

Theorem: name-listp-of-list-fix

(defthm name-listp-of-list-fix
  (implies (name-listp acl2::x)
           (name-listp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: name-listp-of-rev

(defthm name-listp-of-rev
  (equal (name-listp (rev acl2::x))
         (name-listp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: name-listp-of-append

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