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• Dec-digit-char-list*p

Dec-digit-char-list*p-basics

Basic theorems about dec-digit-char-list*p, generated by std::deflist.

Definitions and Theorems

Theorem: dec-digit-char-list*p-of-cons

(defthm dec-digit-char-list*p-of-cons
  (equal (dec-digit-char-list*p (cons a x))
         (and (dec-digit-char-p a)
              (dec-digit-char-list*p x)))
  :rule-classes ((:rewrite)))

Theorem: dec-digit-char-list*p-of-cdr-when-dec-digit-char-list*p

(defthm dec-digit-char-list*p-of-cdr-when-dec-digit-char-list*p
  (implies (dec-digit-char-list*p (double-rewrite x))
           (dec-digit-char-list*p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: dec-digit-char-list*p-when-not-consp

(defthm dec-digit-char-list*p-when-not-consp
  (implies (not (consp x))
           (dec-digit-char-list*p x))
  :rule-classes ((:rewrite)))

Theorem: dec-digit-char-p-of-car-when-dec-digit-char-list*p

(defthm dec-digit-char-p-of-car-when-dec-digit-char-list*p
  (implies (dec-digit-char-list*p x)
           (iff (dec-digit-char-p (car x))
                (or (consp x) (dec-digit-char-p nil))))
  :rule-classes ((:rewrite)))

Theorem: dec-digit-char-list*p-of-append

(defthm dec-digit-char-list*p-of-append
  (equal (dec-digit-char-list*p (append a b))
         (and (dec-digit-char-list*p a)
              (dec-digit-char-list*p b)))
  :rule-classes ((:rewrite)))

Theorem: dec-digit-char-list*p-of-list-fix

(defthm dec-digit-char-list*p-of-list-fix
  (equal (dec-digit-char-list*p (list-fix x))
         (dec-digit-char-list*p x))
  :rule-classes ((:rewrite)))

Theorem: dec-digit-char-list*p-of-rev

(defthm dec-digit-char-list*p-of-rev
  (equal (dec-digit-char-list*p (rev x))
         (dec-digit-char-list*p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: dec-digit-char-list*p-of-take

(defthm dec-digit-char-list*p-of-take
  (implies (dec-digit-char-list*p (double-rewrite x))
           (iff (dec-digit-char-list*p (take n x))
                (or (dec-digit-char-p nil)
                    (<= (nfix n) (len x)))))
  :rule-classes ((:rewrite)))

Theorem: dec-digit-char-list*p-of-nthcdr

(defthm dec-digit-char-list*p-of-nthcdr
  (implies (dec-digit-char-list*p (double-rewrite x))
           (dec-digit-char-list*p (nthcdr n x)))
  :rule-classes ((:rewrite)))

Theorem: dec-digit-char-list*p-of-repeat

(defthm dec-digit-char-list*p-of-repeat
  (iff (dec-digit-char-list*p (repeat n x))
       (or (dec-digit-char-p x) (zp n)))
  :rule-classes ((:rewrite)))