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Segment-driver-map

Segment-driver-map-p

Signature
(segment-driver-map-p x) → *

Definitions and Theorems

Function: segment-driver-map-p

(defun segment-driver-map-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'segment-driver-map-p))
    (declare (ignorable __function__))
    (if (atom x)
        t
      (and (consp (car x))
           (svar-p (caar x))
           (segment-driverlist-p (cdar x))
           (segment-driver-map-p (cdr x))))))

Theorem: segment-driver-map-p-of-repeat

(defthm segment-driver-map-p-of-repeat
  (iff (segment-driver-map-p (repeat acl2::n x))
       (or (and (consp x)
                (svar-p (car x))
                (segment-driverlist-p (cdr x)))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: segment-driver-map-p-of-rev

(defthm segment-driver-map-p-of-rev
  (equal (segment-driver-map-p (rev x))
         (segment-driver-map-p (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: segment-driver-map-p-of-list-fix

(defthm segment-driver-map-p-of-list-fix
  (equal (segment-driver-map-p (list-fix x))
         (segment-driver-map-p x))
  :rule-classes ((:rewrite)))

Theorem: segment-driver-map-p-of-append

(defthm segment-driver-map-p-of-append
  (equal (segment-driver-map-p (append acl2::a acl2::b))
         (and (segment-driver-map-p acl2::a)
              (segment-driver-map-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: segment-driver-map-p-when-not-consp

(defthm segment-driver-map-p-when-not-consp
  (implies (not (consp x))
           (segment-driver-map-p x))
  :rule-classes ((:rewrite)))

Theorem: segment-driver-map-p-of-cdr-when-segment-driver-map-p

(defthm segment-driver-map-p-of-cdr-when-segment-driver-map-p
  (implies (segment-driver-map-p (double-rewrite x))
           (segment-driver-map-p (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: segment-driver-map-p-of-cons

(defthm segment-driver-map-p-of-cons
  (equal (segment-driver-map-p (cons acl2::a x))
         (and (and (consp acl2::a)
                   (svar-p (car acl2::a))
                   (segment-driverlist-p (cdr acl2::a)))
              (segment-driver-map-p x)))
  :rule-classes ((:rewrite)))

Theorem: segment-driver-map-p-of-fast-alist-clean

(defthm segment-driver-map-p-of-fast-alist-clean
  (implies (segment-driver-map-p x)
           (segment-driver-map-p (fast-alist-clean x)))
  :rule-classes ((:rewrite)))

Theorem: segment-driver-map-p-of-hons-shrink-alist

(defthm segment-driver-map-p-of-hons-shrink-alist
  (implies (and (segment-driver-map-p x)
                (segment-driver-map-p y))
           (segment-driver-map-p (hons-shrink-alist x y)))
  :rule-classes ((:rewrite)))

Theorem: segment-driver-map-p-of-hons-acons

(defthm segment-driver-map-p-of-hons-acons
  (equal (segment-driver-map-p (hons-acons acl2::a acl2::n x))
         (and (svar-p acl2::a)
              (segment-driverlist-p acl2::n)
              (segment-driver-map-p x)))
  :rule-classes ((:rewrite)))

Theorem: segment-driverlist-p-of-cdr-of-hons-assoc-equal-when-segment-driver-map-p

(defthm
 segment-driverlist-p-of-cdr-of-hons-assoc-equal-when-segment-driver-map-p
 (implies
      (segment-driver-map-p x)
      (iff (segment-driverlist-p (cdr (hons-assoc-equal acl2::k x)))
           (or (hons-assoc-equal acl2::k x)
               (segment-driverlist-p nil))))
 :rule-classes ((:rewrite)))

Theorem: segment-driverlist-p-of-cdar-when-segment-driver-map-p

(defthm segment-driverlist-p-of-cdar-when-segment-driver-map-p
  (implies (segment-driver-map-p x)
           (iff (segment-driverlist-p (cdar x))
                (or (consp x)
                    (segment-driverlist-p nil))))
  :rule-classes ((:rewrite)))

Theorem: svar-p-of-caar-when-segment-driver-map-p

(defthm svar-p-of-caar-when-segment-driver-map-p
  (implies (segment-driver-map-p x)
           (iff (svar-p (caar x))
                (or (consp x) (svar-p nil))))
  :rule-classes ((:rewrite)))