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Vl-initial

Vl-initial-fix

Fixing function for vl-initial structures.

Signature
(vl-initial-fix x) → new-x
Arguments: x — Guard (vl-initial-p x).
Returns: new-x — Type (vl-initial-p new-x).

Definitions and Theorems

Function: vl-initial-fix$inline

(defun vl-initial-fix$inline (x)
 (declare (xargs :guard (vl-initial-p x)))
 (let ((__function__ 'vl-initial-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((stmt (vl-stmt-fix (std::prod-car (cdr x))))
     (atts (vl-atts-fix (std::prod-car (std::prod-cdr (cdr x)))))
     (loc
         (vl-location-fix (std::prod-cdr (std::prod-cdr (cdr x))))))
    (cons
       :vl-initial (std::prod-cons stmt (std::prod-cons atts loc))))
   :exec x)))

Theorem: vl-initial-p-of-vl-initial-fix

(defthm vl-initial-p-of-vl-initial-fix
  (b* ((new-x (vl-initial-fix$inline x)))
    (vl-initial-p new-x))
  :rule-classes :rewrite)

Theorem: vl-initial-fix-when-vl-initial-p

(defthm vl-initial-fix-when-vl-initial-p
  (implies (vl-initial-p x)
           (equal (vl-initial-fix x) x)))

Function: vl-initial-equiv$inline

(defun vl-initial-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (vl-initial-p acl2::x)
                              (vl-initial-p acl2::y))))
  (equal (vl-initial-fix acl2::x)
         (vl-initial-fix acl2::y)))

Theorem: vl-initial-equiv-is-an-equivalence

(defthm vl-initial-equiv-is-an-equivalence
  (and (booleanp (vl-initial-equiv x y))
       (vl-initial-equiv x x)
       (implies (vl-initial-equiv x y)
                (vl-initial-equiv y x))
       (implies (and (vl-initial-equiv x y)
                     (vl-initial-equiv y z))
                (vl-initial-equiv x z)))
  :rule-classes (:equivalence))

Theorem: vl-initial-equiv-implies-equal-vl-initial-fix-1

(defthm vl-initial-equiv-implies-equal-vl-initial-fix-1
  (implies (vl-initial-equiv acl2::x x-equiv)
           (equal (vl-initial-fix acl2::x)
                  (vl-initial-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vl-initial-fix-under-vl-initial-equiv

(defthm vl-initial-fix-under-vl-initial-equiv
  (vl-initial-equiv (vl-initial-fix acl2::x)
                    acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-vl-initial-fix-1-forward-to-vl-initial-equiv

(defthm equal-of-vl-initial-fix-1-forward-to-vl-initial-equiv
  (implies (equal (vl-initial-fix acl2::x) acl2::y)
           (vl-initial-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-vl-initial-fix-2-forward-to-vl-initial-equiv

(defthm equal-of-vl-initial-fix-2-forward-to-vl-initial-equiv
  (implies (equal acl2::x (vl-initial-fix acl2::y))
           (vl-initial-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: vl-initial-equiv-of-vl-initial-fix-1-forward

(defthm vl-initial-equiv-of-vl-initial-fix-1-forward
  (implies (vl-initial-equiv (vl-initial-fix acl2::x)
                             acl2::y)
           (vl-initial-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: vl-initial-equiv-of-vl-initial-fix-2-forward

(defthm vl-initial-equiv-of-vl-initial-fix-2-forward
  (implies (vl-initial-equiv acl2::x (vl-initial-fix acl2::y))
           (vl-initial-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)