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Fgl-objectlist-p

Fgl-objectlist-p-basics

Basic theorems about fgl-objectlist-p, generated by deflist.

Definitions and Theorems

Theorem: fgl-objectlist-p-of-cons

(defthm fgl-objectlist-p-of-cons
  (equal (fgl-objectlist-p (cons a x))
         (and (fgl-object-p a)
              (fgl-objectlist-p x)))
  :rule-classes ((:rewrite)))

Theorem: fgl-objectlist-p-of-cdr-when-fgl-objectlist-p

(defthm fgl-objectlist-p-of-cdr-when-fgl-objectlist-p
  (implies (fgl-objectlist-p (double-rewrite x))
           (fgl-objectlist-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: fgl-objectlist-p-when-not-consp

(defthm fgl-objectlist-p-when-not-consp
  (implies (not (consp x))
           (equal (fgl-objectlist-p x) (not x)))
  :rule-classes ((:rewrite)))

Theorem: fgl-object-p-of-car-when-fgl-objectlist-p

(defthm fgl-object-p-of-car-when-fgl-objectlist-p
  (implies (fgl-objectlist-p x)
           (fgl-object-p (car x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-fgl-objectlist-p-compound-recognizer

(defthm true-listp-when-fgl-objectlist-p-compound-recognizer
  (implies (fgl-objectlist-p x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: fgl-objectlist-p-of-list-fix

(defthm fgl-objectlist-p-of-list-fix
  (implies (fgl-objectlist-p x)
           (fgl-objectlist-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: fgl-objectlist-p-of-rev

(defthm fgl-objectlist-p-of-rev
  (equal (fgl-objectlist-p (rev x))
         (fgl-objectlist-p (list-fix x)))
  :rule-classes ((:rewrite)))