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• Edgesplit

Vl-alwayslist-edgesplit

(vl-alwayslist-edgesplit x) applies vl-always-edgesplit to every member of the list x, and appends together all the resulting lists.

This is an ordinary defmapappend.

Function: vl-alwayslist-edgesplit

(defun vl-alwayslist-edgesplit (x)
  (declare (xargs :guard (vl-alwayslist-p x)))
  (mbe :logic
       (if (consp x)
           (append (vl-always-edgesplit (car x))
                   (vl-alwayslist-edgesplit (cdr x)))
         nil)
       :exec (reverse (vl-alwayslist-edgesplit-exec x nil))))

Definitions and Theorems

Function: vl-alwayslist-edgesplit-exec

(defun vl-alwayslist-edgesplit-exec (x acc)
  (declare (xargs :guard (vl-alwayslist-p x)))
  (if (consp x)
      (vl-alwayslist-edgesplit-exec
           (cdr x)
           (revappend (vl-always-edgesplit (car x))
                      acc))
    acc))

Function: vl-alwayslist-edgesplit

(defun vl-alwayslist-edgesplit (x)
  (declare (xargs :guard (vl-alwayslist-p x)))
  (mbe :logic
       (if (consp x)
           (append (vl-always-edgesplit (car x))
                   (vl-alwayslist-edgesplit (cdr x)))
         nil)
       :exec (reverse (vl-alwayslist-edgesplit-exec x nil))))

Theorem: vl-alwayslist-edgesplit-exec-removal

(defthm vl-alwayslist-edgesplit-exec-removal
  (equal (vl-alwayslist-edgesplit-exec acl2::x acl2::acc)
         (revappend (vl-alwayslist-edgesplit acl2::x)
                    acl2::acc))
  :rule-classes ((:rewrite)))

Theorem: set-equiv-congruence-over-vl-alwayslist-edgesplit

(defthm set-equiv-congruence-over-vl-alwayslist-edgesplit
  (implies (set-equiv acl2::x acl2::y)
           (set-equiv (vl-alwayslist-edgesplit acl2::x)
                      (vl-alwayslist-edgesplit acl2::y)))
  :rule-classes ((:congruence)))

Theorem: subsetp-of-vl-alwayslist-edgesplit-when-subsetp

(defthm subsetp-of-vl-alwayslist-edgesplit-when-subsetp
  (implies (subsetp acl2::x acl2::y)
           (subsetp (vl-alwayslist-edgesplit acl2::x)
                    (vl-alwayslist-edgesplit acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: member-in-vl-alwayslist-edgesplit

(defthm member-in-vl-alwayslist-edgesplit
  (implies (and (member acl2::k (vl-always-edgesplit acl2::j))
                (member acl2::j acl2::x))
           (member acl2::k
                   (vl-alwayslist-edgesplit acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-alwayslist-edgesplit-of-list-fix

(defthm vl-alwayslist-edgesplit-of-list-fix
  (equal (vl-alwayslist-edgesplit (list-fix acl2::x))
         (vl-alwayslist-edgesplit acl2::x))
  :rule-classes ((:rewrite)))

Theorem: vl-alwayslist-edgesplit-of-append

(defthm vl-alwayslist-edgesplit-of-append
  (equal (vl-alwayslist-edgesplit (append acl2::a acl2::b))
         (append (vl-alwayslist-edgesplit acl2::a)
                 (vl-alwayslist-edgesplit acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: vl-alwayslist-edgesplit-when-not-consp

(defthm vl-alwayslist-edgesplit-when-not-consp
  (implies (not (consp acl2::x))
           (equal (vl-alwayslist-edgesplit acl2::x)
                  nil))
  :rule-classes ((:rewrite)))

Theorem: vl-alwayslist-edgesplit-of-cons

(defthm vl-alwayslist-edgesplit-of-cons
  (equal (vl-alwayslist-edgesplit (cons acl2::a acl2::b))
         (append (vl-always-edgesplit acl2::a)
                 (vl-alwayslist-edgesplit acl2::b)))
  :rule-classes ((:rewrite)))