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• Boolean-array

Boolean-array-fix

Fixing function for boolean-array structures.

Signature

(boolean-array-fix x) → new-x

Arguments

x — Guard (boolean-arrayp x).

Returns

new-x — Type (boolean-arrayp new-x).

Definitions and Theorems

Function: boolean-array-fix$inline

(defun boolean-array-fix$inline (x)
 (declare (xargs :guard (boolean-arrayp x)))
 (let ((__function__ 'boolean-array-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
     ((components (boolean-value-list-fix (std::da-nth 0 (cdr x)))))
     (let ((components (if (< (len components) (expt 2 31))
                           components
                         nil)))
       (cons :boolean-array (list components))))
    :exec x)))

Theorem: boolean-arrayp-of-boolean-array-fix

(defthm boolean-arrayp-of-boolean-array-fix
  (b* ((new-x (boolean-array-fix$inline x)))
    (boolean-arrayp new-x))
  :rule-classes :rewrite)

Theorem: boolean-array-fix-when-boolean-arrayp

(defthm boolean-array-fix-when-boolean-arrayp
  (implies (boolean-arrayp x)
           (equal (boolean-array-fix x) x)))

Function: boolean-array-equiv$inline

(defun boolean-array-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (boolean-arrayp acl2::x)
                              (boolean-arrayp acl2::y))))
  (equal (boolean-array-fix acl2::x)
         (boolean-array-fix acl2::y)))

Theorem: boolean-array-equiv-is-an-equivalence

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

Theorem: boolean-array-equiv-implies-equal-boolean-array-fix-1

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

Theorem: boolean-array-fix-under-boolean-array-equiv

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

Theorem: equal-of-boolean-array-fix-1-forward-to-boolean-array-equiv

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

Theorem: equal-of-boolean-array-fix-2-forward-to-boolean-array-equiv

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

Theorem: boolean-array-equiv-of-boolean-array-fix-1-forward

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

Theorem: boolean-array-equiv-of-boolean-array-fix-2-forward

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