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Visibility

Visibility-fix

Fixing function for visibility structures.

Signature
(visibility-fix x) → new-x
Arguments: x — Guard (visibilityp x).
Returns: new-x — Type (visibilityp new-x).

Definitions and Theorems

Function: visibility-fix$inline

(defun visibility-fix$inline (x)
  (declare (xargs :guard (visibilityp x)))
  (let ((__function__ 'visibility-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (visibility-kind x)
           (:public (cons :public (list)))
           (:private (cons :private (list)))
           (:constant (cons :constant (list))))
         :exec x)))

Theorem: visibilityp-of-visibility-fix

(defthm visibilityp-of-visibility-fix
  (b* ((new-x (visibility-fix$inline x)))
    (visibilityp new-x))
  :rule-classes :rewrite)

Theorem: visibility-fix-when-visibilityp

(defthm visibility-fix-when-visibilityp
  (implies (visibilityp x)
           (equal (visibility-fix x) x)))

Function: visibility-equiv$inline

(defun visibility-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (visibilityp acl2::x)
                              (visibilityp acl2::y))))
  (equal (visibility-fix acl2::x)
         (visibility-fix acl2::y)))

Theorem: visibility-equiv-is-an-equivalence

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

Theorem: visibility-equiv-implies-equal-visibility-fix-1

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

Theorem: visibility-fix-under-visibility-equiv

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

Theorem: equal-of-visibility-fix-1-forward-to-visibility-equiv

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

Theorem: equal-of-visibility-fix-2-forward-to-visibility-equiv

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

Theorem: visibility-equiv-of-visibility-fix-1-forward

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

Theorem: visibility-equiv-of-visibility-fix-2-forward

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

Theorem: visibility-kind$inline-of-visibility-fix-x

(defthm visibility-kind$inline-of-visibility-fix-x
  (equal (visibility-kind$inline (visibility-fix x))
         (visibility-kind$inline x)))

Theorem: visibility-kind$inline-visibility-equiv-congruence-on-x

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

Theorem: consp-of-visibility-fix

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