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Jfield

Jfield-fix

Fixing function for jfield structures.

Signature
(jfield-fix x) → new-x
Arguments: x — Guard (jfieldp x).
Returns: new-x — Type (jfieldp new-x).

Definitions and Theorems

Function: jfield-fix$inline

(defun jfield-fix$inline (x)
  (declare (xargs :guard (jfieldp x)))
  (let ((__function__ 'jfield-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((access (jaccess-fix (cdr (std::da-nth 0 x))))
              (static? (acl2::bool-fix (cdr (std::da-nth 1 x))))
              (final? (acl2::bool-fix (cdr (std::da-nth 2 x))))
              (transient? (acl2::bool-fix (cdr (std::da-nth 3 x))))
              (volatile? (acl2::bool-fix (cdr (std::da-nth 4 x))))
              (type (jtype-fix (cdr (std::da-nth 5 x))))
              (name (str-fix (cdr (std::da-nth 6 x))))
              (init? (maybe-jexpr-fix (cdr (std::da-nth 7 x)))))
           (list (cons 'access access)
                 (cons 'static? static?)
                 (cons 'final? final?)
                 (cons 'transient? transient?)
                 (cons 'volatile? volatile?)
                 (cons 'type type)
                 (cons 'name name)
                 (cons 'init? init?)))
         :exec x)))

Theorem: jfieldp-of-jfield-fix

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

Theorem: jfield-fix-when-jfieldp

(defthm jfield-fix-when-jfieldp
  (implies (jfieldp x)
           (equal (jfield-fix x) x)))

Function: jfield-equiv$inline

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

Theorem: jfield-equiv-is-an-equivalence

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

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

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

Theorem: jfield-fix-under-jfield-equiv

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

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

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

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

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

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

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

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

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