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• Finalizer

Finalizer-equiv

Basic equivalence relation for finalizer structures.

Definitions and Theorems

Function: finalizer-equiv$inline

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

Theorem: finalizer-equiv-is-an-equivalence

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

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

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

Theorem: finalizer-fix-under-finalizer-equiv

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

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

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

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

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

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

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

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

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