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True-list-listp

True-list-listp-basics

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

Definitions and Theorems

Theorem: true-list-listp-of-cons

(defthm true-list-listp-of-cons
  (equal (true-list-listp (cons a x))
         (and (true-listp a)
              (true-list-listp x)))
  :rule-classes ((:rewrite)))

Theorem: true-list-listp-of-cdr-when-true-list-listp

(defthm true-list-listp-of-cdr-when-true-list-listp
  (implies (true-list-listp (double-rewrite x))
           (true-list-listp (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: true-list-listp-when-not-consp

(defthm true-list-listp-when-not-consp
  (implies (not (consp x))
           (equal (true-list-listp x) (not x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-car-when-true-list-listp

(defthm true-listp-of-car-when-true-list-listp
  (implies (true-list-listp x)
           (true-listp (car x)))
  :rule-classes ((:rewrite)))

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

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

Theorem: true-list-listp-of-list-fix

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

Theorem: true-list-listp-of-rev

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