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Char-val-set

Char-val-setp

Recognizer for char-val-set.

Signature
(char-val-setp x) → *

Definitions and Theorems

Function: char-val-setp

(defun char-val-setp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (char-val-p (car x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (acl2::fast-<< (car x) (cadr x))
                  (char-val-setp (cdr x)))))))

Theorem: booleanp-ofchar-val-setp

(defthm booleanp-ofchar-val-setp
  (booleanp (char-val-setp x)))

Theorem: setp-when-char-val-setp

(defthm setp-when-char-val-setp
  (implies (char-val-setp x) (setp x))
  :rule-classes (:rewrite))

Theorem: char-val-p-of-head-when-char-val-setp

(defthm char-val-p-of-head-when-char-val-setp
  (implies (char-val-setp x)
           (equal (char-val-p (head x))
                  (not (emptyp x)))))

Theorem: char-val-setp-of-tail-when-char-val-setp

(defthm char-val-setp-of-tail-when-char-val-setp
  (implies (char-val-setp x)
           (char-val-setp (tail x))))

Theorem: char-val-setp-of-insert

(defthm char-val-setp-of-insert
  (equal (char-val-setp (insert a x))
         (and (char-val-p a)
              (char-val-setp (sfix x)))))

Theorem: char-val-p-when-in-char-val-setp-binds-free-x

(defthm char-val-p-when-in-char-val-setp-binds-free-x
  (implies (and (in a x) (char-val-setp x))
           (char-val-p a)))

Theorem: not-in-char-val-setp-when-not-char-val-p

(defthm not-in-char-val-setp-when-not-char-val-p
  (implies (and (char-val-setp x)
                (not (char-val-p a)))
           (not (in a x))))

Theorem: char-val-setp-of-union

(defthm char-val-setp-of-union
  (equal (char-val-setp (union x y))
         (and (char-val-setp (sfix x))
              (char-val-setp (sfix y)))))

Theorem: char-val-setp-of-intersect

(defthm char-val-setp-of-intersect
  (implies (and (char-val-setp x)
                (char-val-setp y))
           (char-val-setp (intersect x y))))

Theorem: char-val-setp-of-difference

(defthm char-val-setp-of-difference
  (implies (char-val-setp x)
           (char-val-setp (difference x y))))

Theorem: char-val-setp-of-delete

(defthm char-val-setp-of-delete
  (implies (char-val-setp x)
           (char-val-setp (delete a x))))