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Jaccess

Jaccess-fix

Fixing function for jaccess structures.

Signature
(jaccess-fix x) → new-x
Arguments: x — Guard (jaccessp x).
Returns: new-x — Type (jaccessp new-x).

Definitions and Theorems

Function: jaccess-fix$inline

(defun jaccess-fix$inline (x)
  (declare (xargs :guard (jaccessp x)))
  (let ((__function__ 'jaccess-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (jaccess-kind x)
           (:public (cons :public (list)))
           (:protected (cons :protected (list)))
           (:private (cons :private (list)))
           (:default (cons :default (list))))
         :exec x)))

Theorem: jaccessp-of-jaccess-fix

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

Theorem: jaccess-fix-when-jaccessp

(defthm jaccess-fix-when-jaccessp
  (implies (jaccessp x)
           (equal (jaccess-fix x) x)))

Function: jaccess-equiv$inline

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

Theorem: jaccess-equiv-is-an-equivalence

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

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

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

Theorem: jaccess-fix-under-jaccess-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-jaccess-fix

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