Lift bindig/uscore-digit to lists.
(bindig/uscore-digit-list x) → dus
This is an ordinary std::defprojection.
Function:
(defun bindig/uscore-digit-list-exec (x acc) (declare (xargs :guard (bin-digit-listp x))) (let ((__function__ 'bindig/uscore-digit-list-exec)) (declare (ignorable __function__)) (if (consp x) (bindig/uscore-digit-list-exec (cdr x) (cons (bindig/uscore-digit (car x)) acc)) acc)))
Function:
(defun bindig/uscore-digit-list-nrev (x acl2::nrev) (declare (xargs :stobjs (acl2::nrev))) (declare (xargs :guard (bin-digit-listp x))) (let ((__function__ 'bindig/uscore-digit-list-nrev)) (declare (ignorable __function__)) (if (atom x) (acl2::nrev-fix acl2::nrev) (let ((acl2::nrev (acl2::nrev-push (bindig/uscore-digit (car x)) acl2::nrev))) (bindig/uscore-digit-list-nrev (cdr x) acl2::nrev)))))
Function:
(defun bindig/uscore-digit-list (x) (declare (xargs :guard (bin-digit-listp x))) (let ((__function__ 'bindig/uscore-digit-list)) (declare (ignorable __function__)) (mbe :logic (if (consp x) (cons (bindig/uscore-digit (car x)) (bindig/uscore-digit-list (cdr x))) nil) :exec (if (atom x) nil (acl2::with-local-nrev (bindig/uscore-digit-list-nrev x acl2::nrev))))))
Theorem:
(defthm bindig/uscore-listp-of-bindig/uscore-digit-list (b* ((dus (bindig/uscore-digit-list x))) (bindig/uscore-listp dus)) :rule-classes :rewrite)
Theorem:
(defthm bindig/uscore-digit-list-nrev-removal (equal (bindig/uscore-digit-list-nrev acl2::x acl2::nrev) (append acl2::nrev (bindig/uscore-digit-list acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindig/uscore-digit-list-exec-removal (equal (bindig/uscore-digit-list-exec acl2::x acl2::acc) (revappend (bindig/uscore-digit-list acl2::x) acl2::acc)) :rule-classes ((:rewrite)))
Theorem:
(defthm bindig/uscore-digit-list-of-take (implies (<= (nfix acl2::n) (len acl2::x)) (equal (bindig/uscore-digit-list (take acl2::n acl2::x)) (take acl2::n (bindig/uscore-digit-list acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm set-equiv-congruence-over-bindig/uscore-digit-list (implies (set-equiv acl2::x acl2::y) (set-equiv (bindig/uscore-digit-list acl2::x) (bindig/uscore-digit-list acl2::y))) :rule-classes ((:congruence)))
Theorem:
(defthm subsetp-of-bindig/uscore-digit-list-when-subsetp (implies (subsetp acl2::x acl2::y) (subsetp (bindig/uscore-digit-list acl2::x) (bindig/uscore-digit-list acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm member-of-bindig/uscore-digit-in-bindig/uscore-digit-list (implies (member acl2::k acl2::x) (member (bindig/uscore-digit acl2::k) (bindig/uscore-digit-list acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindig/uscore-digit-list-of-rev (equal (bindig/uscore-digit-list (rev acl2::x)) (rev (bindig/uscore-digit-list acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindig/uscore-digit-list-of-list-fix (equal (bindig/uscore-digit-list (list-fix acl2::x)) (bindig/uscore-digit-list acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm bindig/uscore-digit-list-of-append (equal (bindig/uscore-digit-list (append acl2::a acl2::b)) (append (bindig/uscore-digit-list acl2::a) (bindig/uscore-digit-list acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm cdr-of-bindig/uscore-digit-list (equal (cdr (bindig/uscore-digit-list acl2::x)) (bindig/uscore-digit-list (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm car-of-bindig/uscore-digit-list (equal (car (bindig/uscore-digit-list acl2::x)) (and (consp acl2::x) (bindig/uscore-digit (car acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindig/uscore-digit-list-under-iff (iff (bindig/uscore-digit-list acl2::x) (consp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm consp-of-bindig/uscore-digit-list (equal (consp (bindig/uscore-digit-list acl2::x)) (consp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm len-of-bindig/uscore-digit-list (equal (len (bindig/uscore-digit-list acl2::x)) (len acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-of-bindig/uscore-digit-list (true-listp (bindig/uscore-digit-list acl2::x)) :rule-classes :type-prescription)
Theorem:
(defthm bindig/uscore-digit-list-when-not-consp (implies (not (consp acl2::x)) (equal (bindig/uscore-digit-list acl2::x) nil)) :rule-classes ((:rewrite)))
Theorem:
(defthm bindig/uscore-digit-list-of-cons (equal (bindig/uscore-digit-list (cons acl2::a acl2::b)) (cons (bindig/uscore-digit acl2::a) (bindig/uscore-digit-list acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm bindig/uscore-kind-of-car-of-last-of-bindig/uscore-digit-list (implies (consp x) (b* ((?dus (bindig/uscore-digit-list x))) (equal (bindig/uscore-kind (car (last dus))) :digit))))