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Sd-keylist->indicies

(sd-keylist->indicies x) maps sd-key->index across a list.

Signature

(sd-keylist->indicies x) → *

Arguments

x — Guard (sd-keylist-p x).

This is an ordinary defprojection.

Definitions and Theorems

Function: sd-keylist->indicies-exec

(defun sd-keylist->indicies-exec (x acc)
 (declare (xargs :guard (sd-keylist-p x)))
 (declare (xargs :guard t))
 (let ((__function__ 'sd-keylist->indicies-exec))
  (declare (ignorable __function__))
  (if (consp x)
      (sd-keylist->indicies-exec (cdr x)
                                 (cons (sd-key->index (car x)) acc))
    acc)))

Function: sd-keylist->indicies-nrev

(defun sd-keylist->indicies-nrev (x nrev)
  (declare (xargs :stobjs (nrev)))
  (declare (xargs :guard (sd-keylist-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'sd-keylist->indicies-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (nrev-fix nrev)
      (let ((nrev (nrev-push (sd-key->index (car x))
                             nrev)))
        (sd-keylist->indicies-nrev (cdr x)
                                   nrev)))))

Function: sd-keylist->indicies

(defun sd-keylist->indicies (x)
  (declare (xargs :guard (sd-keylist-p x)))
  (declare (xargs :guard t))
  (let ((__function__ 'sd-keylist->indicies))
    (declare (ignorable __function__))
    (mbe :logic
         (if (consp x)
             (cons (sd-key->index (car x))
                   (sd-keylist->indicies (cdr x)))
           nil)
         :exec
         (if (atom x)
             nil
           (with-local-nrev (sd-keylist->indicies-nrev x nrev))))))

Theorem: sd-keylist->indicies-of-update-nth

(defthm sd-keylist->indicies-of-update-nth
 (implies
  (<= (nfix acl2::n) (len acl2::x))
  (equal (sd-keylist->indicies (update-nth acl2::n acl2::v acl2::x))
         (update-nth acl2::n (sd-key->index acl2::v)
                     (sd-keylist->indicies acl2::x))))
 :rule-classes ((:rewrite)))

Theorem: sd-keylist->indicies-of-revappend

(defthm sd-keylist->indicies-of-revappend
  (equal (sd-keylist->indicies (revappend acl2::x acl2::y))
         (revappend (sd-keylist->indicies acl2::x)
                    (sd-keylist->indicies acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: nthcdr-of-sd-keylist->indicies

(defthm nthcdr-of-sd-keylist->indicies
  (equal (nthcdr acl2::n (sd-keylist->indicies acl2::x))
         (sd-keylist->indicies (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: nth-of-sd-keylist->indicies

(defthm nth-of-sd-keylist->indicies
  (equal (nth acl2::n (sd-keylist->indicies acl2::x))
         (and (< (nfix acl2::n) (len acl2::x))
              (sd-key->index (nth acl2::n acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: sd-keylist->indicies-of-take

(defthm sd-keylist->indicies-of-take
  (implies (<= (nfix acl2::n) (len acl2::x))
           (equal (sd-keylist->indicies (take acl2::n acl2::x))
                  (take acl2::n
                        (sd-keylist->indicies acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-sd-keylist->indicies

(defthm set-equiv-congruence-over-sd-keylist->indicies
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (sd-keylist->indicies acl2::x)
                      (sd-keylist->indicies acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-sd-keylist->indicies-when-subsetp

(defthm subsetp-of-sd-keylist->indicies-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (sd-keylist->indicies acl2::x)
                    (sd-keylist->indicies acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-of-sd-key->index-in-sd-keylist->indicies

(defthm member-of-sd-key->index-in-sd-keylist->indicies
  (implies (member acl2::k acl2::x)
           (member (sd-key->index acl2::k)
                   (sd-keylist->indicies acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: sd-keylist->indicies-nrev-removal

(defthm sd-keylist->indicies-nrev-removal
  (equal (sd-keylist->indicies-nrev acl2::x nrev)
         (append nrev (sd-keylist->indicies acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: sd-keylist->indicies-exec-removal

(defthm sd-keylist->indicies-exec-removal
  (equal (sd-keylist->indicies-exec acl2::x acl2::acc)
         (revappend (sd-keylist->indicies acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: sd-keylist->indicies-of-rev

(defthm sd-keylist->indicies-of-rev
  (equal (sd-keylist->indicies (rev acl2::x))
         (rev (sd-keylist->indicies acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: sd-keylist->indicies-of-list-fix

(defthm sd-keylist->indicies-of-list-fix
  (equal (sd-keylist->indicies (list-fix acl2::x))
         (sd-keylist->indicies acl2::x))
  :rule-classes ((:rewrite)))

Theorem: sd-keylist->indicies-of-append

(defthm sd-keylist->indicies-of-append
  (equal (sd-keylist->indicies (append acl2::a acl2::b))
         (append (sd-keylist->indicies acl2::a)
                 (sd-keylist->indicies acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-sd-keylist->indicies

(defthm cdr-of-sd-keylist->indicies
  (equal (cdr (sd-keylist->indicies acl2::x))
         (sd-keylist->indicies (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-sd-keylist->indicies

(defthm car-of-sd-keylist->indicies
  (equal (car (sd-keylist->indicies acl2::x))
         (and (consp acl2::x)
              (sd-key->index (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: sd-keylist->indicies-under-iff

(defthm sd-keylist->indicies-under-iff
  (iff (sd-keylist->indicies acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-sd-keylist->indicies

(defthm consp-of-sd-keylist->indicies
  (equal (consp (sd-keylist->indicies acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-sd-keylist->indicies

(defthm len-of-sd-keylist->indicies
  (equal (len (sd-keylist->indicies acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-sd-keylist->indicies

(defthm true-listp-of-sd-keylist->indicies
  (true-listp (sd-keylist->indicies acl2::x))
  :rule-classes :type-prescription)

Theorem: sd-keylist->indicies-when-not-consp

(defthm sd-keylist->indicies-when-not-consp
  (implies (not (consp acl2::x))
           (equal (sd-keylist->indicies acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: sd-keylist->indicies-of-cons

(defthm sd-keylist->indicies-of-cons
  (equal (sd-keylist->indicies (cons acl2::a acl2::b))
         (cons (sd-key->index acl2::a)
               (sd-keylist->indicies acl2::b)))
  :rule-classes ((:rewrite)))