Lift alternative->name to lists.
(alternative-list->name-list x) → *
This is an ordinary std::defprojection.
Function:
(defun alternative-list->name-list-exec (x acc) (declare (xargs :guard (alternative-listp x))) (declare (xargs :guard t)) (let ((__function__ 'alternative-list->name-list-exec)) (declare (ignorable __function__)) (if (consp x) (alternative-list->name-list-exec (cdr x) (cons (alternative->name (car x)) acc)) acc)))
Function:
(defun alternative-list->name-list-nrev (x acl2::nrev) (declare (xargs :stobjs (acl2::nrev))) (declare (xargs :guard (alternative-listp x))) (declare (xargs :guard t)) (let ((__function__ 'alternative-list->name-list-nrev)) (declare (ignorable __function__)) (if (atom x) (acl2::nrev-fix acl2::nrev) (let ((acl2::nrev (acl2::nrev-push (alternative->name (car x)) acl2::nrev))) (alternative-list->name-list-nrev (cdr x) acl2::nrev)))))
Function:
(defun alternative-list->name-list (x) (declare (xargs :guard (alternative-listp x))) (declare (xargs :guard t)) (let ((__function__ 'alternative-list->name-list)) (declare (ignorable __function__)) (mbe :logic (if (consp x) (cons (alternative->name (car x)) (alternative-list->name-list (cdr x))) nil) :exec (if (atom x) nil (acl2::with-local-nrev (alternative-list->name-list-nrev x acl2::nrev))))))
Theorem:
(defthm nth-of-alternative-list->name-list (equal (nth acl2::n (alternative-list->name-list acl2::x)) (and (< (nfix acl2::n) (len acl2::x)) (alternative->name (nth acl2::n acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-list->name-list-nrev-removal (equal (alternative-list->name-list-nrev acl2::x acl2::nrev) (append acl2::nrev (alternative-list->name-list acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-list->name-list-exec-removal (equal (alternative-list->name-list-exec acl2::x acl2::acc) (revappend (alternative-list->name-list acl2::x) acl2::acc)) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-list->name-list-of-rev (equal (alternative-list->name-list (rev acl2::x)) (rev (alternative-list->name-list acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-list->name-list-of-list-fix (equal (alternative-list->name-list (list-fix acl2::x)) (alternative-list->name-list acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-list->name-list-of-append (equal (alternative-list->name-list (append acl2::a acl2::b)) (append (alternative-list->name-list acl2::a) (alternative-list->name-list acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm cdr-of-alternative-list->name-list (equal (cdr (alternative-list->name-list acl2::x)) (alternative-list->name-list (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm car-of-alternative-list->name-list (equal (car (alternative-list->name-list acl2::x)) (and (consp acl2::x) (alternative->name (car acl2::x)))) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-list->name-list-under-iff (iff (alternative-list->name-list acl2::x) (consp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm consp-of-alternative-list->name-list (equal (consp (alternative-list->name-list acl2::x)) (consp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm len-of-alternative-list->name-list (equal (len (alternative-list->name-list acl2::x)) (len acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-of-alternative-list->name-list (true-listp (alternative-list->name-list acl2::x)) :rule-classes :type-prescription)
Theorem:
(defthm alternative-list->name-list-when-not-consp (implies (not (consp acl2::x)) (equal (alternative-list->name-list acl2::x) nil)) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-list->name-list-of-cons (equal (alternative-list->name-list (cons acl2::a acl2::b)) (cons (alternative->name acl2::a) (alternative-list->name-list acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm identifier-listp-of-alternative-list->name-list (identifier-listp (alternative-list->name-list x)))
Theorem:
(defthm alternative-list->name-list-of-alternative-list-fix-x (equal (alternative-list->name-list (alternative-list-fix x)) (alternative-list->name-list x)))
Theorem:
(defthm alternative-list->name-list-alternative-list-equiv-congruence-on-x (implies (alternative-list-equiv x x-equiv) (equal (alternative-list->name-list x) (alternative-list->name-list x-equiv))) :rule-classes :congruence)