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Svar/4vec-alistlist-p

Svar/4vec-alistlist-p-basics

Basic theorems about svar/4vec-alistlist-p, generated by std::deflist.

Definitions and Theorems

Theorem: svar/4vec-alistlist-p-of-cons

(defthm svar/4vec-alistlist-p-of-cons
  (equal (svar/4vec-alistlist-p (cons acl2::a x))
         (and (svar/4vec-alist-p acl2::a)
              (svar/4vec-alistlist-p x)))
  :rule-classes ((:rewrite)))

Theorem: svar/4vec-alistlist-p-of-cdr-when-svar/4vec-alistlist-p

(defthm svar/4vec-alistlist-p-of-cdr-when-svar/4vec-alistlist-p
  (implies (svar/4vec-alistlist-p (double-rewrite x))
           (svar/4vec-alistlist-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: svar/4vec-alistlist-p-when-not-consp

(defthm svar/4vec-alistlist-p-when-not-consp
  (implies (not (consp x))
           (equal (svar/4vec-alistlist-p x)
                  (not x)))
  :rule-classes ((:rewrite)))

Theorem: svar/4vec-alist-p-of-car-when-svar/4vec-alistlist-p

(defthm svar/4vec-alist-p-of-car-when-svar/4vec-alistlist-p
  (implies (svar/4vec-alistlist-p x)
           (iff (svar/4vec-alist-p (car x))
                (or (consp x) (svar/4vec-alist-p nil))))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-svar/4vec-alistlist-p-compound-recognizer

(defthm true-listp-when-svar/4vec-alistlist-p-compound-recognizer
  (implies (svar/4vec-alistlist-p x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: svar/4vec-alistlist-p-of-list-fix

(defthm svar/4vec-alistlist-p-of-list-fix
  (implies (svar/4vec-alistlist-p x)
           (svar/4vec-alistlist-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: svar/4vec-alistlist-p-of-rev

(defthm svar/4vec-alistlist-p-of-rev
  (equal (svar/4vec-alistlist-p (rev x))
         (svar/4vec-alistlist-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: svar/4vec-alistlist-p-of-repeat

(defthm svar/4vec-alistlist-p-of-repeat
  (iff (svar/4vec-alistlist-p (repeat acl2::n x))
       (or (svar/4vec-alist-p x) (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: svar/4vec-alistlist-p-of-append

(defthm svar/4vec-alistlist-p-of-append
  (equal (svar/4vec-alistlist-p (append acl2::a acl2::b))
         (and (svar/4vec-alistlist-p (list-fix acl2::a))
              (svar/4vec-alistlist-p acl2::b)))
  :rule-classes ((:rewrite)))