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• Values

Member-types-of-member-values

Lift member-type-of-member-value to lists.

Signature

(member-types-of-member-values x) → memtypes

Returns

memtypes — Type (member-type-listp memtypes).

This is an ordinary std::defprojection.

Definitions and Theorems

Function: member-types-of-member-values-exec

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

Function: member-types-of-member-values-nrev

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

Function: member-types-of-member-values

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

Theorem: member-type-listp-of-member-types-of-member-values

(defthm member-type-listp-of-member-types-of-member-values
  (b* ((memtypes (member-types-of-member-values x)))
    (member-type-listp memtypes))
  :rule-classes :rewrite)

Theorem: member-types-of-member-values-of-take

(defthm member-types-of-member-values-of-take
  (implies
       (<= (nfix acl2::n) (len acl2::x))
       (equal (member-types-of-member-values (take acl2::n acl2::x))
              (take acl2::n
                    (member-types-of-member-values acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-member-types-of-member-values

(defthm set-equiv-congruence-over-member-types-of-member-values
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (member-types-of-member-values acl2::x)
                      (member-types-of-member-values acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-member-types-of-member-values-when-subsetp

(defthm subsetp-of-member-types-of-member-values-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (member-types-of-member-values acl2::x)
                    (member-types-of-member-values acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-of-member-type-of-member-value-in-member-types-of-member-values

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

Theorem: member-types-of-member-values-nrev-removal

(defthm member-types-of-member-values-nrev-removal
  (equal (member-types-of-member-values-nrev acl2::x acl2::nrev)
         (append acl2::nrev
                 (member-types-of-member-values acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: member-types-of-member-values-exec-removal

(defthm member-types-of-member-values-exec-removal
  (equal (member-types-of-member-values-exec acl2::x acl2::acc)
         (revappend (member-types-of-member-values acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: member-types-of-member-values-of-rev

(defthm member-types-of-member-values-of-rev
  (equal (member-types-of-member-values (rev acl2::x))
         (rev (member-types-of-member-values acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: member-types-of-member-values-of-list-fix

(defthm member-types-of-member-values-of-list-fix
  (equal (member-types-of-member-values (list-fix acl2::x))
         (member-types-of-member-values acl2::x))
  :rule-classes ((:rewrite)))

Theorem: member-types-of-member-values-of-append

(defthm member-types-of-member-values-of-append
  (equal (member-types-of-member-values (append acl2::a acl2::b))
         (append (member-types-of-member-values acl2::a)
                 (member-types-of-member-values acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-member-types-of-member-values

(defthm cdr-of-member-types-of-member-values
  (equal (cdr (member-types-of-member-values acl2::x))
         (member-types-of-member-values (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-member-types-of-member-values

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

Theorem: member-types-of-member-values-under-iff

(defthm member-types-of-member-values-under-iff
  (iff (member-types-of-member-values acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-member-types-of-member-values

(defthm consp-of-member-types-of-member-values
  (equal (consp (member-types-of-member-values acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-member-types-of-member-values

(defthm len-of-member-types-of-member-values
  (equal (len (member-types-of-member-values acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-member-types-of-member-values

(defthm true-listp-of-member-types-of-member-values
  (true-listp (member-types-of-member-values acl2::x))
  :rule-classes :type-prescription)

Theorem: member-types-of-member-values-when-not-consp

(defthm member-types-of-member-values-when-not-consp
  (implies (not (consp acl2::x))
           (equal (member-types-of-member-values acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: member-types-of-member-values-of-cons

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

Theorem: member-types-of-member-values-of-member-value-list-fix-x

(defthm member-types-of-member-values-of-member-value-list-fix-x
  (equal (member-types-of-member-values (member-value-list-fix x))
         (member-types-of-member-values x)))

Theorem: member-types-of-member-values-member-value-list-equiv-congruence-on-x

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