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Symbol-value-set

Symbol-value-setp

Recognizer for symbol-value-set.

Signature
(symbol-value-setp x) → *

Definitions and Theorems

Function: symbol-value-setp

(defun symbol-value-setp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (symbol-valuep (car x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (acl2::fast-<< (car x) (cadr x))
                  (symbol-value-setp (cdr x)))))))

Theorem: booleanp-ofsymbol-value-setp

(defthm booleanp-ofsymbol-value-setp
  (booleanp (symbol-value-setp x)))

Theorem: setp-when-symbol-value-setp

(defthm setp-when-symbol-value-setp
  (implies (symbol-value-setp x) (setp x))
  :rule-classes (:rewrite))

Theorem: symbol-valuep-of-head-when-symbol-value-setp

(defthm symbol-valuep-of-head-when-symbol-value-setp
  (implies (symbol-value-setp x)
           (equal (symbol-valuep (head x))
                  (not (emptyp x)))))

Theorem: symbol-value-setp-of-tail-when-symbol-value-setp

(defthm symbol-value-setp-of-tail-when-symbol-value-setp
  (implies (symbol-value-setp x)
           (symbol-value-setp (tail x))))

Theorem: symbol-value-setp-of-insert

(defthm symbol-value-setp-of-insert
  (equal (symbol-value-setp (insert a x))
         (and (symbol-valuep a)
              (symbol-value-setp (sfix x)))))

Theorem: symbol-valuep-when-in-symbol-value-setp-binds-free-x

(defthm symbol-valuep-when-in-symbol-value-setp-binds-free-x
  (implies (and (in a x) (symbol-value-setp x))
           (symbol-valuep a)))

Theorem: not-in-symbol-value-setp-when-not-symbol-valuep

(defthm not-in-symbol-value-setp-when-not-symbol-valuep
  (implies (and (symbol-value-setp x)
                (not (symbol-valuep a)))
           (not (in a x))))

Theorem: symbol-value-setp-of-union

(defthm symbol-value-setp-of-union
  (equal (symbol-value-setp (union x y))
         (and (symbol-value-setp (sfix x))
              (symbol-value-setp (sfix y)))))

Theorem: symbol-value-setp-of-intersect

(defthm symbol-value-setp-of-intersect
  (implies (and (symbol-value-setp x)
                (symbol-value-setp y))
           (symbol-value-setp (intersect x y))))

Theorem: symbol-value-setp-of-difference

(defthm symbol-value-setp-of-difference
  (implies (symbol-value-setp x)
           (symbol-value-setp (difference x y))))

Theorem: symbol-value-setp-of-delete

(defthm symbol-value-setp-of-delete
  (implies (symbol-value-setp x)
           (symbol-value-setp (delete a x))))