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• Vl-namedb

Vl-namedb-fix

Fixing function for vl-namedb structures.

Signature

(vl-namedb-fix x) → new-x

Arguments

x — Guard (vl-namedb-p x).

Returns

new-x — Type (vl-namedb-p new-x).

Definitions and Theorems

Function: vl-namedb-fix$inline

(defun vl-namedb-fix$inline (x)
 (declare (xargs :guard (vl-namedb-p x)))
 (let ((__function__ 'vl-namedb-fix))
  (declare (ignorable __function__))
  (mbe
      :logic
      (b* ((names (vl-namedb-nameset-fix (std::prod-car (cdr x))))
           (pmap (vl-namedb-prefixmap-fix
                      (std::prod-car (std::prod-cdr (cdr x)))))
           (pset (vl-namedb-nameset-fix
                      (std::prod-cdr (std::prod-cdr (cdr x))))))
        (let ((pmap (vl-namedb-pmap-fix names pmap))
              (pset (vl-namedb-pset-fix names pmap pset)))
          (cons :vl-namedb
                (std::prod-cons names (std::prod-cons pmap pset)))))
      :exec x)))

Theorem: vl-namedb-p-of-vl-namedb-fix

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

Theorem: vl-namedb-fix-when-vl-namedb-p

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

Function: vl-namedb-equiv$inline

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

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

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

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

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

Theorem: vl-namedb-fix-under-vl-namedb-equiv

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

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

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

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

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

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

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

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

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