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• Decimal-integer-literals

Decdig/uscore-digit-list

Lift decdig/uscore-digit to lists.

Signature

(decdig/uscore-digit-list x) → dus

Returns

dus — Type (decdig/uscore-listp dus).

This is an ordinary std::defprojection.

Definitions and Theorems

Function: decdig/uscore-digit-list-exec

(defun decdig/uscore-digit-list-exec (x acc)
  (declare (xargs :guard (dec-digit-listp x)))
  (let ((__function__ 'decdig/uscore-digit-list-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (decdig/uscore-digit-list-exec
             (cdr x)
             (cons (decdig/uscore-digit (car x))
                   acc))
      acc)))

Function: decdig/uscore-digit-list-nrev

(defun decdig/uscore-digit-list-nrev (x acl2::nrev)
 (declare (xargs :stobjs (acl2::nrev)))
 (declare (xargs :guard (dec-digit-listp x)))
 (let ((__function__ 'decdig/uscore-digit-list-nrev))
  (declare (ignorable __function__))
  (if (atom x)
      (acl2::nrev-fix acl2::nrev)
    (let ((acl2::nrev (acl2::nrev-push (decdig/uscore-digit (car x))
                                       acl2::nrev)))
      (decdig/uscore-digit-list-nrev (cdr x)
                                     acl2::nrev)))))

Function: decdig/uscore-digit-list

(defun decdig/uscore-digit-list (x)
  (declare (xargs :guard (dec-digit-listp x)))
  (let ((__function__ 'decdig/uscore-digit-list))
    (declare (ignorable __function__))
    (mbe :logic
         (if (consp x)
             (cons (decdig/uscore-digit (car x))
                   (decdig/uscore-digit-list (cdr x)))
           nil)
         :exec
         (if (atom x)
             nil
           (acl2::with-local-nrev
                (decdig/uscore-digit-list-nrev x acl2::nrev))))))

Theorem: decdig/uscore-listp-of-decdig/uscore-digit-list

(defthm decdig/uscore-listp-of-decdig/uscore-digit-list
  (b* ((dus (decdig/uscore-digit-list x)))
    (decdig/uscore-listp dus))
  :rule-classes :rewrite)

Theorem: decdig/uscore-digit-list-nrev-removal

(defthm decdig/uscore-digit-list-nrev-removal
  (equal (decdig/uscore-digit-list-nrev acl2::x acl2::nrev)
         (append acl2::nrev
                 (decdig/uscore-digit-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: decdig/uscore-digit-list-exec-removal

(defthm decdig/uscore-digit-list-exec-removal
  (equal (decdig/uscore-digit-list-exec acl2::x acl2::acc)
         (revappend (decdig/uscore-digit-list acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: decdig/uscore-digit-list-of-take

(defthm decdig/uscore-digit-list-of-take
  (implies (<= (nfix acl2::n) (len acl2::x))
           (equal (decdig/uscore-digit-list (take acl2::n acl2::x))
                  (take acl2::n
                        (decdig/uscore-digit-list acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-decdig/uscore-digit-list

(defthm set-equiv-congruence-over-decdig/uscore-digit-list
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (decdig/uscore-digit-list acl2::x)
                      (decdig/uscore-digit-list acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-decdig/uscore-digit-list-when-subsetp

(defthm subsetp-of-decdig/uscore-digit-list-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (decdig/uscore-digit-list acl2::x)
                    (decdig/uscore-digit-list acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-of-decdig/uscore-digit-in-decdig/uscore-digit-list

(defthm member-of-decdig/uscore-digit-in-decdig/uscore-digit-list
  (implies (member acl2::k acl2::x)
           (member (decdig/uscore-digit acl2::k)
                   (decdig/uscore-digit-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: decdig/uscore-digit-list-of-rev

(defthm decdig/uscore-digit-list-of-rev
  (equal (decdig/uscore-digit-list (rev acl2::x))
         (rev (decdig/uscore-digit-list acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: decdig/uscore-digit-list-of-list-fix

(defthm decdig/uscore-digit-list-of-list-fix
  (equal (decdig/uscore-digit-list (list-fix acl2::x))
         (decdig/uscore-digit-list acl2::x))
  :rule-classes ((:rewrite)))

Theorem: decdig/uscore-digit-list-of-append

(defthm decdig/uscore-digit-list-of-append
  (equal (decdig/uscore-digit-list (append acl2::a acl2::b))
         (append (decdig/uscore-digit-list acl2::a)
                 (decdig/uscore-digit-list acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-decdig/uscore-digit-list

(defthm cdr-of-decdig/uscore-digit-list
  (equal (cdr (decdig/uscore-digit-list acl2::x))
         (decdig/uscore-digit-list (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-decdig/uscore-digit-list

(defthm car-of-decdig/uscore-digit-list
  (equal (car (decdig/uscore-digit-list acl2::x))
         (and (consp acl2::x)
              (decdig/uscore-digit (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: decdig/uscore-digit-list-under-iff

(defthm decdig/uscore-digit-list-under-iff
  (iff (decdig/uscore-digit-list acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-decdig/uscore-digit-list

(defthm consp-of-decdig/uscore-digit-list
  (equal (consp (decdig/uscore-digit-list acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-decdig/uscore-digit-list

(defthm len-of-decdig/uscore-digit-list
  (equal (len (decdig/uscore-digit-list acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-decdig/uscore-digit-list

(defthm true-listp-of-decdig/uscore-digit-list
  (true-listp (decdig/uscore-digit-list acl2::x))
  :rule-classes :type-prescription)

Theorem: decdig/uscore-digit-list-when-not-consp

(defthm decdig/uscore-digit-list-when-not-consp
  (implies (not (consp acl2::x))
           (equal (decdig/uscore-digit-list acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: decdig/uscore-digit-list-of-cons

(defthm decdig/uscore-digit-list-of-cons
  (equal (decdig/uscore-digit-list (cons acl2::a acl2::b))
         (cons (decdig/uscore-digit acl2::a)
               (decdig/uscore-digit-list acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: decdig/uscore-kind-of-car-of-last-of-decdig/uscore-digit-list

(defthm
      decdig/uscore-kind-of-car-of-last-of-decdig/uscore-digit-list
  (implies (consp x)
           (b* ((?dus (decdig/uscore-digit-list x)))
             (equal (decdig/uscore-kind (car (last dus)))
                    :digit))))