		Search-engine friendly clone of the ACL2 documentation.

Svl-occ

Svl-occ-fix

Fixing function for svl-occ structures.

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

Definitions and Theorems

Function: svl-occ-fix$inline

(defun svl-occ-fix$inline (x)
 (declare (xargs :guard (svl-occ-p x)))
 (let ((acl2::__function__ 'svl-occ-fix))
  (declare (ignorable acl2::__function__))
  (mbe
   :logic
   (case (svl-occ-kind x)
    (:assign (b* ((output (sv::svar-fix (std::da-nth 0 (cdr x))))
                  (svex (svex-fix (std::da-nth 1 (cdr x)))))
               (cons :assign (list output svex))))
    (:module
         (b* ((inputs (sv::svexlist-fix (std::da-nth 0 (cdr x))))
              (outputs (wire-list-list-fix (std::da-nth 1 (cdr x))))
              (name (sv::modname-fix (std::da-nth 2 (cdr x)))))
           (cons :module (list inputs outputs name)))))
   :exec x)))

Theorem: svl-occ-p-of-svl-occ-fix

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

Theorem: svl-occ-fix-when-svl-occ-p

(defthm svl-occ-fix-when-svl-occ-p
  (implies (svl-occ-p x)
           (equal (svl-occ-fix x) x)))

Function: svl-occ-equiv$inline

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

Theorem: svl-occ-equiv-is-an-equivalence

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

Theorem: svl-occ-equiv-implies-equal-svl-occ-fix-1

(defthm svl-occ-equiv-implies-equal-svl-occ-fix-1
  (implies (svl-occ-equiv acl2::x x-equiv)
           (equal (svl-occ-fix acl2::x)
                  (svl-occ-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: svl-occ-fix-under-svl-occ-equiv

(defthm svl-occ-fix-under-svl-occ-equiv
  (svl-occ-equiv (svl-occ-fix acl2::x)
                 acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-svl-occ-fix-1-forward-to-svl-occ-equiv

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

Theorem: equal-of-svl-occ-fix-2-forward-to-svl-occ-equiv

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

Theorem: svl-occ-equiv-of-svl-occ-fix-1-forward

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

Theorem: svl-occ-equiv-of-svl-occ-fix-2-forward

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

Theorem: svl-occ-kind$inline-of-svl-occ-fix-x

(defthm svl-occ-kind$inline-of-svl-occ-fix-x
  (equal (svl-occ-kind$inline (svl-occ-fix x))
         (svl-occ-kind$inline x)))

Theorem: svl-occ-kind$inline-svl-occ-equiv-congruence-on-x

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

Theorem: consp-of-svl-occ-fix

(defthm consp-of-svl-occ-fix
  (consp (svl-occ-fix x))
  :rule-classes :type-prescription)