		Search-engine friendly clone of the ACL2 documentation.

Symbol-listp

Symbol-listp-basics

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

Definitions and Theorems

Theorem: symbol-listp-of-cons

(defthm symbol-listp-of-cons
        (equal (symbol-listp (cons a x))
               (and (symbolp a) (symbol-listp x)))
        :rule-classes ((:rewrite)))

Theorem: symbol-listp-of-cdr-when-symbol-listp

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

Theorem: symbol-listp-when-not-consp

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

Theorem: symbolp-of-car-when-symbol-listp

(defthm symbolp-of-car-when-symbol-listp
        (implies (symbol-listp x)
                 (symbolp (car x)))
        :rule-classes ((:rewrite)))

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

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

Theorem: symbol-listp-of-list-fix

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

Theorem: symbol-listp-of-rev

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