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• Vl-defaultskew-item

Vl-defaultskew-item-fix

Fixing function for vl-defaultskew-item structures.

Signature

(vl-defaultskew-item-fix x) → new-x

Arguments

x — Guard (vl-defaultskew-item-p x).

Returns

new-x — Type (vl-defaultskew-item-p new-x).

Definitions and Theorems

Function: vl-defaultskew-item-fix$inline

(defun vl-defaultskew-item-fix$inline (x)
  (declare (xargs :guard (vl-defaultskew-item-p x)))
  (let ((__function__ 'vl-defaultskew-item-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((inputp (acl2::bool-fix (std::prod-car (cdr x))))
              (skew (vl-clkskew-fix (std::prod-cdr (cdr x)))))
           (cons :vl-defaultskew (std::prod-cons inputp skew)))
         :exec x)))

Theorem: vl-defaultskew-item-p-of-vl-defaultskew-item-fix

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

Theorem: vl-defaultskew-item-fix-when-vl-defaultskew-item-p

(defthm vl-defaultskew-item-fix-when-vl-defaultskew-item-p
  (implies (vl-defaultskew-item-p x)
           (equal (vl-defaultskew-item-fix x) x)))

Function: vl-defaultskew-item-equiv$inline

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

Theorem: vl-defaultskew-item-equiv-is-an-equivalence

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

Theorem: vl-defaultskew-item-equiv-implies-equal-vl-defaultskew-item-fix-1

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

Theorem: vl-defaultskew-item-fix-under-vl-defaultskew-item-equiv

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

Theorem: equal-of-vl-defaultskew-item-fix-1-forward-to-vl-defaultskew-item-equiv

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

Theorem: equal-of-vl-defaultskew-item-fix-2-forward-to-vl-defaultskew-item-equiv

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

Theorem: vl-defaultskew-item-equiv-of-vl-defaultskew-item-fix-1-forward

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

Theorem: vl-defaultskew-item-equiv-of-vl-defaultskew-item-fix-2-forward

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