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ACL2-number-listp

ACL2-number-listp-basics

Basic theorems about ACL2-number-listp, generated by std::deflist.

Definitions and Theorems

Theorem: acl2-number-listp-of-cons

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

Theorem: acl2-number-listp-of-cdr-when-acl2-number-listp

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

Theorem: acl2-number-listp-when-not-consp

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

Theorem: acl2-numberp-of-car-when-acl2-number-listp

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

Theorem: true-listp-when-acl2-number-listp-compound-recognizer

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

Theorem: acl2-number-listp-of-list-fix

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

Theorem: acl2-number-listp-of-rev

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