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Svl-module

Svl-module-fix

Fixing function for svl-module structures.

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

Definitions and Theorems

Function: svl-module-fix$inline

(defun svl-module-fix$inline (x)
 (declare (xargs :guard (svl-module-p x)))
 (let ((acl2::__function__ 'svl-module-fix))
  (declare (ignorable acl2::__function__))
  (mbe
    :logic
    (b* ((rank (nfix (cdr (std::da-nth 0 x))))
         (inputs (wire-list-fix (cdr (std::da-nth 1 x))))
         (delayed-inputs (sv::svarlist-fix (cdr (std::da-nth 2 x))))
         (outputs (wire-list-fix (cdr (std::da-nth 3 x))))
         (occs (svl-occ-alist-fix (cdr (std::da-nth 4 x)))))
      (list (cons 'rank rank)
            (cons 'inputs inputs)
            (cons 'delayed-inputs delayed-inputs)
            (cons 'outputs outputs)
            (cons 'occs occs)))
    :exec x)))

Theorem: svl-module-p-of-svl-module-fix

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

Theorem: svl-module-fix-when-svl-module-p

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

Function: svl-module-equiv$inline

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

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

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

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

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

Theorem: svl-module-fix-under-svl-module-equiv

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

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

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

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

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

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

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

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

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