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• Eviscconfig

Eviscconfig-fix

Fixing function for eviscconfig structures.

Signature

(eviscconfig-fix x) → new-x

Arguments

x — Guard (eviscconfig-p x).

Returns

new-x — Type (eviscconfig-p new-x).

Definitions and Theorems

Function: eviscconfig-fix$inline

(defun eviscconfig-fix$inline (x)
 (declare (xargs :guard (eviscconfig-p x)))
 (let ((acl2::__function__ 'eviscconfig-fix))
  (declare (ignorable acl2::__function__))
  (mbe
   :logic
   (b* ((print-level (acl2::maybe-natp-fix (car (car (cdr x)))))
        (print-length (acl2::maybe-natp-fix (cdr (car (cdr x)))))
        (replacement-alist (car (cdr (cdr x))))
        (hiding-cars (cdr (cdr (cdr x)))))
    (cons :eviscconfig (cons (cons print-level print-length)
                             (cons replacement-alist hiding-cars))))
   :exec x)))

Theorem: eviscconfig-p-of-eviscconfig-fix

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

Theorem: eviscconfig-fix-when-eviscconfig-p

(defthm eviscconfig-fix-when-eviscconfig-p
  (implies (eviscconfig-p x)
           (equal (eviscconfig-fix x) x)))

Function: eviscconfig-equiv$inline

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

Theorem: eviscconfig-equiv-is-an-equivalence

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

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

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

Theorem: eviscconfig-fix-under-eviscconfig-equiv

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

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

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

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

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

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

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

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

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