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• Inline-mods

Vl-inline-mod-in-mods-aux

(vl-inline-mod-in-mods-aux sub x) maps vl-inline-mod-in-mod across a list.

Signature

(vl-inline-mod-in-mods-aux sub x) → *

This is an ordinary defprojection.

Definitions and Theorems

Function: vl-inline-mod-in-mods-aux-exec

(defun vl-inline-mod-in-mods-aux-exec (sub x acc)
  (declare (xargs :guard (and (vl-module-p sub)
                              (vl-ok-to-inline-p sub)
                              (vl-modulelist-p x))))
  (let ((__function__ 'vl-inline-mod-in-mods-aux-exec))
    (declare (ignorable __function__))
    (if (consp x)
        (vl-inline-mod-in-mods-aux-exec
             sub (cdr x)
             (cons (vl-inline-mod-in-mod sub (car x))
                   acc))
      acc)))

Function: vl-inline-mod-in-mods-aux-nrev

(defun vl-inline-mod-in-mods-aux-nrev (sub x nrev)
  (declare (xargs :stobjs (nrev)))
  (declare (xargs :guard (and (vl-module-p sub)
                              (vl-ok-to-inline-p sub)
                              (vl-modulelist-p x))))
  (let ((__function__ 'vl-inline-mod-in-mods-aux-nrev))
    (declare (ignorable __function__))
    (if (atom x)
        (nrev-fix nrev)
      (let ((nrev (nrev-push (vl-inline-mod-in-mod sub (car x))
                             nrev)))
        (vl-inline-mod-in-mods-aux-nrev sub (cdr x)
                                        nrev)))))

Function: vl-inline-mod-in-mods-aux

(defun vl-inline-mod-in-mods-aux (sub x)
  (declare (xargs :guard (and (vl-module-p sub)
                              (vl-ok-to-inline-p sub)
                              (vl-modulelist-p x))))
  (let ((__function__ 'vl-inline-mod-in-mods-aux))
    (declare (ignorable __function__))
    (mbe :logic
         (if (consp x)
             (cons (vl-inline-mod-in-mod sub (car x))
                   (vl-inline-mod-in-mods-aux sub (cdr x)))
           nil)
         :exec
         (if (atom x)
             nil
           (with-local-nrev
                (vl-inline-mod-in-mods-aux-nrev sub x nrev))))))

Theorem: vl-inline-mod-in-mods-aux-of-update-nth

(defthm vl-inline-mod-in-mods-aux-of-update-nth
 (implies
  (<= (nfix acl2::n) (len acl2::x))
  (equal
    (vl-inline-mod-in-mods-aux sub
                               (update-nth acl2::n acl2::v acl2::x))
    (update-nth acl2::n
                (vl-inline-mod-in-mod sub acl2::v)
                (vl-inline-mod-in-mods-aux sub acl2::x))))
 :rule-classes ((:rewrite)))

Theorem: vl-inline-mod-in-mods-aux-of-revappend

(defthm vl-inline-mod-in-mods-aux-of-revappend
  (equal (vl-inline-mod-in-mods-aux sub (revappend acl2::x acl2::y))
         (revappend (vl-inline-mod-in-mods-aux sub acl2::x)
                    (vl-inline-mod-in-mods-aux sub acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: nthcdr-of-vl-inline-mod-in-mods-aux

(defthm nthcdr-of-vl-inline-mod-in-mods-aux
  (equal (nthcdr acl2::n
                 (vl-inline-mod-in-mods-aux sub acl2::x))
         (vl-inline-mod-in-mods-aux sub (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: nth-of-vl-inline-mod-in-mods-aux

(defthm nth-of-vl-inline-mod-in-mods-aux
  (equal (nth acl2::n
              (vl-inline-mod-in-mods-aux sub acl2::x))
         (and (< (nfix acl2::n) (len acl2::x))
              (vl-inline-mod-in-mod sub (nth acl2::n acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-inline-mod-in-mods-aux-nrev-removal

(defthm vl-inline-mod-in-mods-aux-nrev-removal
  (equal (vl-inline-mod-in-mods-aux-nrev sub acl2::x nrev)
         (append nrev
                 (vl-inline-mod-in-mods-aux sub acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-inline-mod-in-mods-aux-exec-removal

(defthm vl-inline-mod-in-mods-aux-exec-removal
  (equal (vl-inline-mod-in-mods-aux-exec sub acl2::x acl2::acc)
         (revappend (vl-inline-mod-in-mods-aux sub acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: vl-inline-mod-in-mods-aux-of-take

(defthm vl-inline-mod-in-mods-aux-of-take
  (implies
       (<= (nfix acl2::n) (len acl2::x))
       (equal (vl-inline-mod-in-mods-aux sub (take acl2::n acl2::x))
              (take acl2::n
                    (vl-inline-mod-in-mods-aux sub acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-vl-inline-mod-in-mods-aux

(defthm set-equiv-congruence-over-vl-inline-mod-in-mods-aux
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (vl-inline-mod-in-mods-aux sub acl2::x)
                      (vl-inline-mod-in-mods-aux sub acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-vl-inline-mod-in-mods-aux-when-subsetp

(defthm subsetp-of-vl-inline-mod-in-mods-aux-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (vl-inline-mod-in-mods-aux sub acl2::x)
                    (vl-inline-mod-in-mods-aux sub acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-of-vl-inline-mod-in-mod-in-vl-inline-mod-in-mods-aux

(defthm member-of-vl-inline-mod-in-mod-in-vl-inline-mod-in-mods-aux
  (implies (member acl2::k acl2::x)
           (member (vl-inline-mod-in-mod sub acl2::k)
                   (vl-inline-mod-in-mods-aux sub acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-inline-mod-in-mods-aux-of-rev

(defthm vl-inline-mod-in-mods-aux-of-rev
  (equal (vl-inline-mod-in-mods-aux sub (rev acl2::x))
         (rev (vl-inline-mod-in-mods-aux sub acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-inline-mod-in-mods-aux-of-list-fix

(defthm vl-inline-mod-in-mods-aux-of-list-fix
  (equal (vl-inline-mod-in-mods-aux sub (list-fix acl2::x))
         (vl-inline-mod-in-mods-aux sub acl2::x))
  :rule-classes ((:rewrite)))

Theorem: vl-inline-mod-in-mods-aux-of-append

(defthm vl-inline-mod-in-mods-aux-of-append
  (equal (vl-inline-mod-in-mods-aux sub (append acl2::a acl2::b))
         (append (vl-inline-mod-in-mods-aux sub acl2::a)
                 (vl-inline-mod-in-mods-aux sub acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: cdr-of-vl-inline-mod-in-mods-aux

(defthm cdr-of-vl-inline-mod-in-mods-aux
  (equal (cdr (vl-inline-mod-in-mods-aux sub acl2::x))
         (vl-inline-mod-in-mods-aux sub (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: car-of-vl-inline-mod-in-mods-aux

(defthm car-of-vl-inline-mod-in-mods-aux
  (equal (car (vl-inline-mod-in-mods-aux sub acl2::x))
         (and (consp acl2::x)
              (vl-inline-mod-in-mod sub (car acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-inline-mod-in-mods-aux-under-iff

(defthm vl-inline-mod-in-mods-aux-under-iff
  (iff (vl-inline-mod-in-mods-aux sub acl2::x)
       (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: consp-of-vl-inline-mod-in-mods-aux

(defthm consp-of-vl-inline-mod-in-mods-aux
  (equal (consp (vl-inline-mod-in-mods-aux sub acl2::x))
         (consp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: len-of-vl-inline-mod-in-mods-aux

(defthm len-of-vl-inline-mod-in-mods-aux
  (equal (len (vl-inline-mod-in-mods-aux sub acl2::x))
         (len acl2::x))
  :rule-classes ((:rewrite)))

Theorem: true-listp-of-vl-inline-mod-in-mods-aux

(defthm true-listp-of-vl-inline-mod-in-mods-aux
  (true-listp (vl-inline-mod-in-mods-aux sub acl2::x))
  :rule-classes :type-prescription)

Theorem: vl-inline-mod-in-mods-aux-when-not-consp

(defthm vl-inline-mod-in-mods-aux-when-not-consp
  (implies (not (consp acl2::x))
           (equal (vl-inline-mod-in-mods-aux sub acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: vl-inline-mod-in-mods-aux-of-cons

(defthm vl-inline-mod-in-mods-aux-of-cons
  (equal (vl-inline-mod-in-mods-aux sub (cons acl2::a acl2::b))
         (cons (vl-inline-mod-in-mod sub acl2::a)
               (vl-inline-mod-in-mods-aux sub acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: vl-modulelist-p-of-vl-inline-mod-in-mods-aux

(defthm vl-modulelist-p-of-vl-inline-mod-in-mods-aux
  (implies (force (and (vl-module-p sub)
                       (vl-ok-to-inline-p sub)
                       (vl-modulelist-p x)))
           (vl-modulelist-p (vl-inline-mod-in-mods-aux sub x))))