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