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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)))