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Vl-namedparamvalue

Vl-namedparamvalue-fix

Fixing function for vl-namedparamvalue structures.

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

Definitions and Theorems

Function: vl-namedparamvalue-fix$inline

(defun vl-namedparamvalue-fix$inline (x)
 (declare (xargs :guard (vl-namedparamvalue-p x)))
 (let ((__function__ 'vl-namedparamvalue-fix))
  (declare (ignorable __function__))
  (mbe
     :logic
     (b* ((name (str-fix (std::prod-car (cdr x))))
          (value (vl-maybe-paramvalue-fix (std::prod-cdr (cdr x)))))
       (cons :vl-namedparamvalue (std::prod-cons name value)))
     :exec x)))

Theorem: vl-namedparamvalue-p-of-vl-namedparamvalue-fix

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

Theorem: vl-namedparamvalue-fix-when-vl-namedparamvalue-p

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

Function: vl-namedparamvalue-equiv$inline

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

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

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

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

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

Theorem: vl-namedparamvalue-fix-under-vl-namedparamvalue-equiv

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

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

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

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

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

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

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

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

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