Lift `type-of-value` to lists.

- Signature
(type-list-of-value-list x) → types

- Returns
`types`—Type (type-listp types) .

This is an ordinary std::defprojection.

**Function: **

(defun type-list-of-value-list-exec (x acc) (declare (xargs :guard (value-listp x))) (let ((__function__ 'type-list-of-value-list-exec)) (declare (ignorable __function__)) (if (consp x) (type-list-of-value-list-exec (cdr x) (cons (type-of-value (car x)) acc)) acc)))

**Function: **

(defun type-list-of-value-list-nrev (x acl2::nrev) (declare (xargs :stobjs (acl2::nrev))) (declare (xargs :guard (value-listp x))) (let ((__function__ 'type-list-of-value-list-nrev)) (declare (ignorable __function__)) (if (atom x) (acl2::nrev-fix acl2::nrev) (let ((acl2::nrev (acl2::nrev-push (type-of-value (car x)) acl2::nrev))) (type-list-of-value-list-nrev (cdr x) acl2::nrev)))))

**Function: **

(defun type-list-of-value-list (x) (declare (xargs :guard (value-listp x))) (let ((__function__ 'type-list-of-value-list)) (declare (ignorable __function__)) (mbe :logic (if (consp x) (cons (type-of-value (car x)) (type-list-of-value-list (cdr x))) nil) :exec (if (atom x) nil (acl2::with-local-nrev (type-list-of-value-list-nrev x acl2::nrev))))))

**Theorem: **

(defthm type-listp-of-type-list-of-value-list (b* ((types (type-list-of-value-list x))) (type-listp types)) :rule-classes :rewrite)

**Theorem: **

(defthm type-list-of-value-list-of-take (implies (<= (nfix acl2::n) (len acl2::x)) (equal (type-list-of-value-list (take acl2::n acl2::x)) (take acl2::n (type-list-of-value-list acl2::x)))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm set-equiv-congruence-over-type-list-of-value-list (implies (set-equiv acl2::x acl2::y) (set-equiv (type-list-of-value-list acl2::x) (type-list-of-value-list acl2::y))) :rule-classes ((:congruence)))

**Theorem: **

(defthm subsetp-of-type-list-of-value-list-when-subsetp (implies (subsetp acl2::x acl2::y) (subsetp (type-list-of-value-list acl2::x) (type-list-of-value-list acl2::y))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm member-of-type-of-value-in-type-list-of-value-list (implies (common-lisp::member acl2::k acl2::x) (common-lisp::member (type-of-value acl2::k) (type-list-of-value-list acl2::x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm type-list-of-value-list-nrev-removal (equal (type-list-of-value-list-nrev acl2::x acl2::nrev) (append acl2::nrev (type-list-of-value-list acl2::x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm type-list-of-value-list-exec-removal (equal (type-list-of-value-list-exec acl2::x acl2::acc) (revappend (type-list-of-value-list acl2::x) acl2::acc)) :rule-classes ((:rewrite)))

**Theorem: **

(defthm type-list-of-value-list-of-rev (equal (type-list-of-value-list (rev acl2::x)) (rev (type-list-of-value-list acl2::x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm type-list-of-value-list-of-list-fix (equal (type-list-of-value-list (list-fix acl2::x)) (type-list-of-value-list acl2::x)) :rule-classes ((:rewrite)))

**Theorem: **

(defthm type-list-of-value-list-of-append (equal (type-list-of-value-list (append acl2::a acl2::b)) (append (type-list-of-value-list acl2::a) (type-list-of-value-list acl2::b))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm cdr-of-type-list-of-value-list (equal (cdr (type-list-of-value-list acl2::x)) (type-list-of-value-list (cdr acl2::x))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm car-of-type-list-of-value-list (equal (car (type-list-of-value-list acl2::x)) (and (consp acl2::x) (type-of-value (car acl2::x)))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm type-list-of-value-list-under-iff (iff (type-list-of-value-list acl2::x) (consp acl2::x)) :rule-classes ((:rewrite)))

**Theorem: **

(defthm consp-of-type-list-of-value-list (equal (consp (type-list-of-value-list acl2::x)) (consp acl2::x)) :rule-classes ((:rewrite)))

**Theorem: **

(defthm len-of-type-list-of-value-list (equal (len (type-list-of-value-list acl2::x)) (len acl2::x)) :rule-classes ((:rewrite)))

**Theorem: **

(defthm true-listp-of-type-list-of-value-list (true-listp (type-list-of-value-list acl2::x)) :rule-classes :type-prescription)

**Theorem: **

(defthm type-list-of-value-list-when-not-consp (implies (not (consp acl2::x)) (equal (type-list-of-value-list acl2::x) nil)) :rule-classes ((:rewrite)))

**Theorem: **

(defthm type-list-of-value-list-of-cons (equal (type-list-of-value-list (cons acl2::a acl2::b)) (cons (type-of-value acl2::a) (type-list-of-value-list acl2::b))) :rule-classes ((:rewrite)))

**Theorem: **

(defthm type-list-of-value-list-of-value-list-fix-x (equal (type-list-of-value-list (value-list-fix x)) (type-list-of-value-list x)))

**Theorem: **

(defthm type-list-of-value-list-value-list-equiv-congruence-on-x (implies (value-list-equiv x x-equiv) (equal (type-list-of-value-list x) (type-list-of-value-list x-equiv))) :rule-classes :congruence)