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Fgl-object-bindings

Fgl-object-bindings-p

Signature
(fgl-object-bindings-p x) → *

Definitions and Theorems

Function: fgl-object-bindings-p

(defun fgl-object-bindings-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'fgl-object-bindings-p))
    (declare (ignorable __function__))
    (if (atom x)
        (eq x nil)
      (and (consp (car x))
           (pseudo-var-p (caar x))
           (fgl-object-p (cdar x))
           (fgl-object-bindings-p (cdr x))))))

Theorem: fgl-object-bindings-p-of-rev

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

Theorem: fgl-object-bindings-p-of-list-fix

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

Theorem: true-listp-when-fgl-object-bindings-p-compound-recognizer

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

Theorem: fgl-object-bindings-p-when-not-consp

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

Theorem: fgl-object-bindings-p-of-cdr-when-fgl-object-bindings-p

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

Theorem: fgl-object-bindings-p-of-cons

(defthm fgl-object-bindings-p-of-cons
  (equal (fgl-object-bindings-p (cons a x))
         (and (and (consp a)
                   (pseudo-var-p (car a))
                   (fgl-object-p (cdr a)))
              (fgl-object-bindings-p x)))
  :rule-classes ((:rewrite)))

Theorem: fgl-object-bindings-p-of-remove-assoc

(defthm fgl-object-bindings-p-of-remove-assoc
  (implies (fgl-object-bindings-p x)
           (fgl-object-bindings-p (remove-assoc-equal name x)))
  :rule-classes ((:rewrite)))

Theorem: fgl-object-bindings-p-of-put-assoc

(defthm fgl-object-bindings-p-of-put-assoc
 (implies
     (and (fgl-object-bindings-p x))
     (iff (fgl-object-bindings-p (put-assoc-equal name acl2::val x))
          (and (pseudo-var-p name)
               (fgl-object-p acl2::val))))
 :rule-classes ((:rewrite)))

Theorem: fgl-object-bindings-p-of-fast-alist-clean

(defthm fgl-object-bindings-p-of-fast-alist-clean
  (implies (fgl-object-bindings-p x)
           (fgl-object-bindings-p (fast-alist-clean x)))
  :rule-classes ((:rewrite)))

Theorem: fgl-object-bindings-p-of-hons-shrink-alist

(defthm fgl-object-bindings-p-of-hons-shrink-alist
  (implies (and (fgl-object-bindings-p x)
                (fgl-object-bindings-p y))
           (fgl-object-bindings-p (hons-shrink-alist x y)))
  :rule-classes ((:rewrite)))

Theorem: fgl-object-bindings-p-of-hons-acons

(defthm fgl-object-bindings-p-of-hons-acons
  (equal (fgl-object-bindings-p (hons-acons a n x))
         (and (pseudo-var-p a)
              (fgl-object-p n)
              (fgl-object-bindings-p x)))
  :rule-classes ((:rewrite)))

Theorem: fgl-object-p-of-cdr-of-hons-assoc-equal-when-fgl-object-bindings-p

(defthm
 fgl-object-p-of-cdr-of-hons-assoc-equal-when-fgl-object-bindings-p
 (implies (fgl-object-bindings-p x)
          (iff (fgl-object-p (cdr (hons-assoc-equal k x)))
               (or (hons-assoc-equal k x)
                   (fgl-object-p nil))))
 :rule-classes ((:rewrite)))

Theorem: alistp-when-fgl-object-bindings-p-rewrite

(defthm alistp-when-fgl-object-bindings-p-rewrite
  (implies (fgl-object-bindings-p x)
           (alistp x))
  :rule-classes ((:rewrite)))

Theorem: alistp-when-fgl-object-bindings-p

(defthm alistp-when-fgl-object-bindings-p
  (implies (fgl-object-bindings-p x)
           (alistp x))
  :rule-classes :tau-system)

Theorem: fgl-object-p-of-cdar-when-fgl-object-bindings-p

(defthm fgl-object-p-of-cdar-when-fgl-object-bindings-p
  (implies (fgl-object-bindings-p x)
           (iff (fgl-object-p (cdar x))
                (or (consp x) (fgl-object-p nil))))
  :rule-classes ((:rewrite)))

Theorem: pseudo-var-p-of-caar-when-fgl-object-bindings-p

(defthm pseudo-var-p-of-caar-when-fgl-object-bindings-p
  (implies (fgl-object-bindings-p x)
           (iff (pseudo-var-p (caar x))
                (or (consp x) (pseudo-var-p nil))))
  :rule-classes ((:rewrite)))