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Jimport

Jimport-fix

Fixing function for jimport structures.

Signature
(jimport-fix x) → new-x
Arguments: x — Guard (jimportp x).
Returns: new-x — Type (jimportp new-x).

Definitions and Theorems

Function: jimport-fix$inline

(defun jimport-fix$inline (x)
  (declare (xargs :guard (jimportp x)))
  (let ((__function__ 'jimport-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((static? (acl2::bool-fix (cdr (std::da-nth 0 x))))
              (target (str-fix (cdr (std::da-nth 1 x)))))
           (list (cons 'static? static?)
                 (cons 'target target)))
         :exec x)))

Theorem: jimportp-of-jimport-fix

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

Theorem: jimport-fix-when-jimportp

(defthm jimport-fix-when-jimportp
  (implies (jimportp x)
           (equal (jimport-fix x) x)))

Function: jimport-equiv$inline

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

Theorem: jimport-equiv-is-an-equivalence

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

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

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

Theorem: jimport-fix-under-jimport-equiv

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

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

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

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

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

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

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

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

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