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Vl-shadowcheck-state

Vl-shadowcheck-state-fix

Fixing function for vl-shadowcheck-state structures.

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

Definitions and Theorems

Function: vl-shadowcheck-state-fix$inline

(defun vl-shadowcheck-state-fix$inline (x)
 (declare (xargs :guard (vl-shadowcheck-state-p x)))
 (let ((__function__ 'vl-shadowcheck-state-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (b*
    ((lexscopes (vl-lexscopes-fix (std::prod-car (cdr x))))
     (ss
        (vl-scopestack-fix (std::prod-car (std::prod-cdr (cdr x)))))
     (design
          (vl-design-fix (std::prod-cdr (std::prod-cdr (cdr x))))))
    (cons :vl-shadowcheck-state
          (std::prod-cons lexscopes (std::prod-cons ss design))))
   :exec x)))

Theorem: vl-shadowcheck-state-p-of-vl-shadowcheck-state-fix

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

Theorem: vl-shadowcheck-state-fix-when-vl-shadowcheck-state-p

(defthm vl-shadowcheck-state-fix-when-vl-shadowcheck-state-p
  (implies (vl-shadowcheck-state-p x)
           (equal (vl-shadowcheck-state-fix x) x)))

Function: vl-shadowcheck-state-equiv$inline

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

Theorem: vl-shadowcheck-state-equiv-is-an-equivalence

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

Theorem: vl-shadowcheck-state-equiv-implies-equal-vl-shadowcheck-state-fix-1

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

Theorem: vl-shadowcheck-state-fix-under-vl-shadowcheck-state-equiv

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

Theorem: equal-of-vl-shadowcheck-state-fix-1-forward-to-vl-shadowcheck-state-equiv

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

Theorem: equal-of-vl-shadowcheck-state-fix-2-forward-to-vl-shadowcheck-state-equiv

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

Theorem: vl-shadowcheck-state-equiv-of-vl-shadowcheck-state-fix-1-forward

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

Theorem: vl-shadowcheck-state-equiv-of-vl-shadowcheck-state-fix-2-forward

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