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• Vl-maybe-scopeitem

Vl-maybe-scopeitem-fix

Fixing function for vl-maybe-scopeitem structures.

Signature

(vl-maybe-scopeitem-fix x) → new-x

Arguments

x — Guard (vl-maybe-scopeitem-p x).

Returns

new-x — Type (vl-maybe-scopeitem-p new-x).

Definitions and Theorems

Function: vl-maybe-scopeitem-fix$inline

(defun vl-maybe-scopeitem-fix$inline (x)
  (declare (xargs :guard (vl-maybe-scopeitem-p x)))
  (let ((__function__ 'vl-maybe-scopeitem-fix))
    (declare (ignorable __function__))
    (mbe :logic (cond ((not x) nil)
                      (t (b* ((fty::val (vl-scopeitem-fix x)))
                           fty::val)))
         :exec x)))

Theorem: vl-maybe-scopeitem-p-of-vl-maybe-scopeitem-fix

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

Theorem: vl-maybe-scopeitem-fix-when-vl-maybe-scopeitem-p

(defthm vl-maybe-scopeitem-fix-when-vl-maybe-scopeitem-p
  (implies (vl-maybe-scopeitem-p x)
           (equal (vl-maybe-scopeitem-fix x) x)))

Function: vl-maybe-scopeitem-equiv$inline

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

Theorem: vl-maybe-scopeitem-equiv-is-an-equivalence

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

Theorem: vl-maybe-scopeitem-equiv-implies-equal-vl-maybe-scopeitem-fix-1

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

Theorem: vl-maybe-scopeitem-fix-under-vl-maybe-scopeitem-equiv

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

Theorem: equal-of-vl-maybe-scopeitem-fix-1-forward-to-vl-maybe-scopeitem-equiv

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

Theorem: equal-of-vl-maybe-scopeitem-fix-2-forward-to-vl-maybe-scopeitem-equiv

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

Theorem: vl-maybe-scopeitem-equiv-of-vl-maybe-scopeitem-fix-1-forward

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

Theorem: vl-maybe-scopeitem-equiv-of-vl-maybe-scopeitem-fix-2-forward

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