		Search-engine friendly clone of the ACL2 documentation.

Comm-listp

Comm-listp-basics

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

Definitions and Theorems

Theorem: comm-listp-of-cons

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

Theorem: comm-listp-of-cdr-when-comm-listp

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

Theorem: comm-listp-when-not-consp

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

Theorem: commp-of-car-when-comm-listp

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

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

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

Theorem: comm-listp-of-list-fix

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

Theorem: comm-listp-of-rev

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

Theorem: comm-listp-of-append

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