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Rewriting

Svex-simpconfig-fix

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

Definitions and Theorems

Function: svex-simpconfig-fix

(defun svex-simpconfig-fix (x)
  (declare (xargs :guard (svex-simpconfig-p x)))
  (let ((__function__ 'svex-simpconfig-fix))
    (declare (ignorable __function__))
    (mbe :logic (svex-simpconfig-fix! x)
         :exec x)))

Theorem: svex-simpconfig-p-of-svex-simpconfig-fix

(defthm svex-simpconfig-p-of-svex-simpconfig-fix
  (b* ((new-x (svex-simpconfig-fix x)))
    (svex-simpconfig-p new-x))
  :rule-classes :rewrite)

Theorem: svex-simpconfig-fix-when-svex-simpconfig-p

(defthm svex-simpconfig-fix-when-svex-simpconfig-p
  (b* ((?new-x (svex-simpconfig-fix x)))
    (implies (svex-simpconfig-p x)
             (equal new-x x))))

Function: svex-simpconfig-equiv$inline

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

Theorem: svex-simpconfig-equiv-is-an-equivalence

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

Theorem: svex-simpconfig-equiv-implies-equal-svex-simpconfig-fix-1

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

Theorem: svex-simpconfig-fix-under-svex-simpconfig-equiv

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

Theorem: svex-simpconfig-fix!-is-fix

(defthm svex-simpconfig-fix!-is-fix
  (equal (svex-simpconfig-fix! x)
         (svex-simpconfig-fix x)))