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Vl-elabkey

Vl-elabkey-fix

Fixing function for vl-elabkey structures.

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

Definitions and Theorems

Function: vl-elabkey-fix$inline

(defun vl-elabkey-fix$inline (x)
  (declare (xargs :guard (vl-elabkey-p x)))
  (let ((__function__ 'vl-elabkey-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (common-lisp::case (vl-elabkey-kind x)
           (:package (b* ((name (str-fix (cdr x))))
                       (hons :package name)))
           (:class (b* ((name (str-fix (cdr x))))
                     (hons :class name)))
           (:item (b* ((name (str-fix (cdr x))))
                    (hons :item name)))
           (:index (b* ((val (ifix (cdr x))))
                     (hons :index val)))
           (:def (b* ((name (str-fix (cdr x))))
                   (hons :def name))))
         :exec x)))

Theorem: vl-elabkey-p-of-vl-elabkey-fix

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

Theorem: vl-elabkey-fix-when-vl-elabkey-p

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

Function: vl-elabkey-equiv$inline

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

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

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

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

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

Theorem: vl-elabkey-fix-under-vl-elabkey-equiv

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

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

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

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

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

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

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

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

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

Theorem: vl-elabkey-kind$inline-of-vl-elabkey-fix-x

(defthm vl-elabkey-kind$inline-of-vl-elabkey-fix-x
  (equal (vl-elabkey-kind$inline (vl-elabkey-fix x))
         (vl-elabkey-kind$inline x)))

Theorem: vl-elabkey-kind$inline-vl-elabkey-equiv-congruence-on-x

(defthm vl-elabkey-kind$inline-vl-elabkey-equiv-congruence-on-x
  (implies (vl-elabkey-equiv x x-equiv)
           (equal (vl-elabkey-kind$inline x)
                  (vl-elabkey-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-vl-elabkey-fix

(defthm consp-of-vl-elabkey-fix
  (consp (vl-elabkey-fix x))
  :rule-classes :type-prescription)