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Data-item

Data-item-fix

Fixing function for data-item structures.

Signature
(data-item-fix x) → new-x
Arguments: x — Guard (data-item-p x).
Returns: new-x — Type (data-item-p new-x).

Definitions and Theorems

Function: data-item-fix$inline

(defun data-item-fix$inline (x)
 (declare (xargs :guard (data-item-p x)))
 (let ((__function__ 'data-item-fix))
   (declare (ignorable __function__))
   (mbe :logic
        (b* ((name (plain-string-fix (cdr (std::da-nth 0 (cdr x)))))
             (value (data-value-fix (cdr (std::da-nth 1 (cdr x))))))
          (cons :data (list (cons 'name name)
                            (cons 'value value))))
        :exec x)))

Theorem: data-item-p-of-data-item-fix

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

Theorem: data-item-fix-when-data-item-p

(defthm data-item-fix-when-data-item-p
  (implies (data-item-p x)
           (equal (data-item-fix x) x)))

Function: data-item-equiv$inline

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

Theorem: data-item-equiv-is-an-equivalence

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

Theorem: data-item-equiv-implies-equal-data-item-fix-1

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

Theorem: data-item-fix-under-data-item-equiv

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

Theorem: equal-of-data-item-fix-1-forward-to-data-item-equiv

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

Theorem: equal-of-data-item-fix-2-forward-to-data-item-equiv

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

Theorem: data-item-equiv-of-data-item-fix-1-forward

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

Theorem: data-item-equiv-of-data-item-fix-2-forward

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