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• Vl-genvar

Vl-genvar-fix

Fixing function for vl-genvar structures.

Signature

(vl-genvar-fix x) → new-x

Arguments

x — Guard (vl-genvar-p x).

Returns

new-x — Type (vl-genvar-p new-x).

Definitions and Theorems

Function: vl-genvar-fix$inline

(defun vl-genvar-fix$inline (x)
  (declare (xargs :guard (vl-genvar-p x)))
  (let ((__function__ 'vl-genvar-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((name (str-fix (cdr (std::da-nth 0 (cdr x)))))
              (atts (vl-atts-fix (cdr (std::da-nth 1 (cdr x)))))
              (loc (vl-location-fix (cdr (std::da-nth 2 (cdr x))))))
           (cons :vl-genvar (list (cons 'name name)
                                  (cons 'atts atts)
                                  (cons 'loc loc))))
         :exec x)))

Theorem: vl-genvar-p-of-vl-genvar-fix

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

Theorem: vl-genvar-fix-when-vl-genvar-p

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

Function: vl-genvar-equiv$inline

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

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

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

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

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

Theorem: vl-genvar-fix-under-vl-genvar-equiv

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

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

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

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

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

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

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

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

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