(vl-define-formallist->defaults x) maps vl-define-formal->default across a list.
(vl-define-formallist->defaults x) → defaults
This is an ordinary defprojection.
Function:
(defun vl-define-formallist->defaults-exec (x acc) (declare (xargs :guard (vl-define-formallist-p x))) (declare (xargs :guard t)) (let ((__function__ 'vl-define-formallist->defaults-exec)) (declare (ignorable __function__)) (if (consp x) (vl-define-formallist->defaults-exec (cdr x) (cons (vl-define-formal->default (car x)) acc)) acc)))
Function:
(defun vl-define-formallist->defaults-nrev (x nrev) (declare (xargs :stobjs (nrev))) (declare (xargs :guard (vl-define-formallist-p x))) (declare (xargs :guard t)) (let ((__function__ 'vl-define-formallist->defaults-nrev)) (declare (ignorable __function__)) (if (atom x) (nrev-fix nrev) (let ((nrev (nrev-push (vl-define-formal->default (car x)) nrev))) (vl-define-formallist->defaults-nrev (cdr x) nrev)))))
Function:
(defun vl-define-formallist->defaults (x) (declare (xargs :guard (vl-define-formallist-p x))) (declare (xargs :guard t)) (let ((__function__ 'vl-define-formallist->defaults)) (declare (ignorable __function__)) (mbe :logic (if (consp x) (cons (vl-define-formal->default (car x)) (vl-define-formallist->defaults (cdr x))) nil) :exec (if (atom x) nil (with-local-nrev (vl-define-formallist->defaults-nrev x nrev))))))
Theorem:
(defthm string-listp-of-vl-define-formallist->defaults (b* ((defaults (vl-define-formallist->defaults x))) (string-listp defaults)) :rule-classes :rewrite)
Theorem:
(defthm vl-define-formallist->defaults-of-vl-define-formallist-fix-x (equal (vl-define-formallist->defaults (vl-define-formallist-fix x)) (vl-define-formallist->defaults x)))
Theorem:
(defthm vl-define-formallist->defaults-vl-define-formallist-equiv-congruence-on-x (implies (vl-define-formallist-equiv x x-equiv) (equal (vl-define-formallist->defaults x) (vl-define-formallist->defaults x-equiv))) :rule-classes :congruence)
Theorem:
(defthm vl-define-formallist->defaults-of-update-nth (implies (<= (nfix acl2::n) (len acl2::x)) (equal (vl-define-formallist->defaults (update-nth acl2::n acl2::v acl2::x)) (update-nth acl2::n (vl-define-formal->default acl2::v) (vl-define-formallist->defaults acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-define-formallist->defaults-of-revappend (equal (vl-define-formallist->defaults (revappend acl2::x acl2::y)) (revappend (vl-define-formallist->defaults acl2::x) (vl-define-formallist->defaults acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm nthcdr-of-vl-define-formallist->defaults (equal (nthcdr acl2::n (vl-define-formallist->defaults acl2::x)) (vl-define-formallist->defaults (nthcdr acl2::n acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm nth-of-vl-define-formallist->defaults (equal (nth acl2::n (vl-define-formallist->defaults acl2::x)) (and (< (nfix acl2::n) (len acl2::x)) (vl-define-formal->default (nth acl2::n acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-define-formallist->defaults-nrev-removal (equal (vl-define-formallist->defaults-nrev acl2::x nrev) (append nrev (vl-define-formallist->defaults acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-define-formallist->defaults-exec-removal (equal (vl-define-formallist->defaults-exec acl2::x acl2::acc) (revappend (vl-define-formallist->defaults acl2::x) acl2::acc)) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-define-formallist->defaults-of-take (implies (<= (nfix acl2::n) (len acl2::x)) (equal (vl-define-formallist->defaults (take acl2::n acl2::x)) (take acl2::n (vl-define-formallist->defaults acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm set-equiv-congruence-over-vl-define-formallist->defaults (implies (set-equiv acl2::x acl2::y) (set-equiv (vl-define-formallist->defaults acl2::x) (vl-define-formallist->defaults acl2::y))) :rule-classes ((:congruence)))
Theorem:
(defthm subsetp-of-vl-define-formallist->defaults-when-subsetp (implies (subsetp acl2::x acl2::y) (subsetp (vl-define-formallist->defaults acl2::x) (vl-define-formallist->defaults acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm member-of-vl-define-formal->default-in-vl-define-formallist->defaults (implies (member acl2::k acl2::x) (member (vl-define-formal->default acl2::k) (vl-define-formallist->defaults acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-define-formallist->defaults-of-rev (equal (vl-define-formallist->defaults (rev acl2::x)) (rev (vl-define-formallist->defaults acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-define-formallist->defaults-of-list-fix (equal (vl-define-formallist->defaults (list-fix acl2::x)) (vl-define-formallist->defaults acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-define-formallist->defaults-of-append (equal (vl-define-formallist->defaults (append acl2::a acl2::b)) (append (vl-define-formallist->defaults acl2::a) (vl-define-formallist->defaults acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm cdr-of-vl-define-formallist->defaults (equal (cdr (vl-define-formallist->defaults acl2::x)) (vl-define-formallist->defaults (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm car-of-vl-define-formallist->defaults (equal (car (vl-define-formallist->defaults acl2::x)) (and (consp acl2::x) (vl-define-formal->default (car acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-define-formallist->defaults-under-iff (iff (vl-define-formallist->defaults acl2::x) (consp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm consp-of-vl-define-formallist->defaults (equal (consp (vl-define-formallist->defaults acl2::x)) (consp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm len-of-vl-define-formallist->defaults (equal (len (vl-define-formallist->defaults acl2::x)) (len acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-of-vl-define-formallist->defaults (true-listp (vl-define-formallist->defaults acl2::x)) :rule-classes :type-prescription)
Theorem:
(defthm vl-define-formallist->defaults-when-not-consp (implies (not (consp acl2::x)) (equal (vl-define-formallist->defaults acl2::x) nil)) :rule-classes ((:rewrite)))
Theorem:
(defthm vl-define-formallist->defaults-of-cons (equal (vl-define-formallist->defaults (cons acl2::a acl2::b)) (cons (vl-define-formal->default acl2::a) (vl-define-formallist->defaults acl2::b))) :rule-classes ((:rewrite)))