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• Vls-commands

Vls-command-args-to-eformals

(vls-command-args-to-eformals x) maps vls-command-arg-to-eformal across a list.

Signature

(vls-command-args-to-eformals x) → *

Arguments

x — Guard (symbol-listp x).

This is an ordinary defprojection.

Definitions and Theorems

Function: vls-command-args-to-eformals-exec

(defun vls-command-args-to-eformals-exec (x acc)
  (declare (xargs :guard (symbol-listp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'vls-command-args-to-eformals-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (vls-command-args-to-eformals-exec
             (cdr x)
             (cons (vls-command-arg-to-eformal (car x))
                   acc))
      acc)))

Function: vls-command-args-to-eformals-nrev

(defun vls-command-args-to-eformals-nrev (x nrev)
  (declare (xargs :stobjs (nrev)))
  (declare (xargs :guard (symbol-listp x)))
  (declare (xargs :guard t))
  (let ((__function__ 'vls-command-args-to-eformals-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (nrev-fix nrev)
      (let ((nrev (nrev-push (vls-command-arg-to-eformal (car x))
                             nrev)))
        (vls-command-args-to-eformals-nrev (cdr x)
                                           nrev)))))

Function: vls-command-args-to-eformals

(defun vls-command-args-to-eformals (x)
 (declare (xargs :guard (symbol-listp x)))
 (declare (xargs :guard t))
 (let ((__function__ 'vls-command-args-to-eformals))
  (declare (ignorable __function__))
  (mbe
   :logic
   (if (consp x)
       (cons (vls-command-arg-to-eformal (car x))
             (vls-command-args-to-eformals (cdr x)))
     nil)
   :exec
   (if (atom x)
       nil
    (with-local-nrev (vls-command-args-to-eformals-nrev x nrev))))))

Theorem: vls-command-args-to-eformals-of-update-nth

(defthm vls-command-args-to-eformals-of-update-nth
  (implies
       (<= (nfix acl2::n) (len acl2::x))
       (equal (vls-command-args-to-eformals
                   (update-nth acl2::n acl2::v acl2::x))
              (update-nth acl2::n
                          (vls-command-arg-to-eformal acl2::v)
                          (vls-command-args-to-eformals acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vls-command-args-to-eformals-of-revappend

(defthm vls-command-args-to-eformals-of-revappend
  (equal (vls-command-args-to-eformals (revappend acl2::x acl2::y))
         (revappend (vls-command-args-to-eformals acl2::x)
                    (vls-command-args-to-eformals acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: nthcdr-of-vls-command-args-to-eformals

(defthm nthcdr-of-vls-command-args-to-eformals
  (equal (nthcdr acl2::n
                 (vls-command-args-to-eformals acl2::x))
         (vls-command-args-to-eformals (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: nth-of-vls-command-args-to-eformals

(defthm nth-of-vls-command-args-to-eformals
  (equal (nth acl2::n
              (vls-command-args-to-eformals acl2::x))
         (and (< (nfix acl2::n) (len acl2::x))
              (vls-command-arg-to-eformal (nth acl2::n acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vls-command-args-to-eformals-nrev-removal

(defthm vls-command-args-to-eformals-nrev-removal
  (equal (vls-command-args-to-eformals-nrev acl2::x nrev)
         (append nrev
                 (vls-command-args-to-eformals acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vls-command-args-to-eformals-exec-removal

(defthm vls-command-args-to-eformals-exec-removal
  (equal (vls-command-args-to-eformals-exec acl2::x acl2::acc)
         (revappend (vls-command-args-to-eformals acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: vls-command-args-to-eformals-of-take

(defthm vls-command-args-to-eformals-of-take
  (implies
       (<= (nfix acl2::n) (len acl2::x))
       (equal (vls-command-args-to-eformals (take acl2::n acl2::x))
              (take acl2::n
                    (vls-command-args-to-eformals acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-vls-command-args-to-eformals

(defthm set-equiv-congruence-over-vls-command-args-to-eformals
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (vls-command-args-to-eformals acl2::x)
                      (vls-command-args-to-eformals acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-vls-command-args-to-eformals-when-subsetp

(defthm subsetp-of-vls-command-args-to-eformals-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (vls-command-args-to-eformals acl2::x)
                    (vls-command-args-to-eformals acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-of-vls-command-arg-to-eformal-in-vls-command-args-to-eformals

(defthm
 member-of-vls-command-arg-to-eformal-in-vls-command-args-to-eformals
 (implies (member acl2::k acl2::x)
          (member (vls-command-arg-to-eformal acl2::k)
                  (vls-command-args-to-eformals acl2::x)))
 :rule-classes ((:rewrite)))

Theorem: vls-command-args-to-eformals-of-rev

(defthm vls-command-args-to-eformals-of-rev
  (equal (vls-command-args-to-eformals (rev acl2::x))
         (rev (vls-command-args-to-eformals acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vls-command-args-to-eformals-of-list-fix

(defthm vls-command-args-to-eformals-of-list-fix
  (equal (vls-command-args-to-eformals (list-fix acl2::x))
         (vls-command-args-to-eformals acl2::x))
  :rule-classes ((:rewrite)))

Theorem: vls-command-args-to-eformals-of-append

(defthm vls-command-args-to-eformals-of-append
  (equal (vls-command-args-to-eformals (append acl2::a acl2::b))
         (append (vls-command-args-to-eformals acl2::a)
                 (vls-command-args-to-eformals acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-vls-command-args-to-eformals

(defthm cdr-of-vls-command-args-to-eformals
  (equal (cdr (vls-command-args-to-eformals acl2::x))
         (vls-command-args-to-eformals (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-vls-command-args-to-eformals

(defthm car-of-vls-command-args-to-eformals
  (equal (car (vls-command-args-to-eformals acl2::x))
         (and (consp acl2::x)
              (vls-command-arg-to-eformal (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vls-command-args-to-eformals-under-iff

(defthm vls-command-args-to-eformals-under-iff
  (iff (vls-command-args-to-eformals acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-vls-command-args-to-eformals

(defthm consp-of-vls-command-args-to-eformals
  (equal (consp (vls-command-args-to-eformals acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-vls-command-args-to-eformals

(defthm len-of-vls-command-args-to-eformals
  (equal (len (vls-command-args-to-eformals acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-vls-command-args-to-eformals

(defthm true-listp-of-vls-command-args-to-eformals
  (true-listp (vls-command-args-to-eformals acl2::x))
  :rule-classes :type-prescription)

Theorem: vls-command-args-to-eformals-when-not-consp

(defthm vls-command-args-to-eformals-when-not-consp
  (implies (not (consp acl2::x))
           (equal (vls-command-args-to-eformals acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: vls-command-args-to-eformals-of-cons

(defthm vls-command-args-to-eformals-of-cons
  (equal (vls-command-args-to-eformals (cons acl2::a acl2::b))
         (cons (vls-command-arg-to-eformal acl2::a)
               (vls-command-args-to-eformals acl2::b)))
  :rule-classes ((:rewrite)))