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Finalize-output

Finalize-output-fix

Fixing function for finalize-output structures.

Signature
(finalize-output-fix x) → new-x
Arguments: x — Guard (finalizer-outputp x).
Returns: new-x — Type (finalizer-outputp new-x).

Definitions and Theorems

Function: finalize-output-fix$inline

(defun finalize-output-fix$inline (x)
  (declare (xargs :guard (finalizer-outputp x)))
  (let ((__function__ 'finalize-output-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((reg (regaccess-fix (cdr (std::da-nth 0 (cdr x)))))
              (type (value-type-fix (cdr (std::da-nth 1 (cdr x))))))
           (cons :finalizer-output (list (cons 'reg reg)
                                         (cons 'type type))))
         :exec x)))

Theorem: finalizer-outputp-of-finalize-output-fix

(defthm finalizer-outputp-of-finalize-output-fix
  (b* ((new-x (finalize-output-fix$inline x)))
    (finalizer-outputp new-x))
  :rule-classes :rewrite)

Theorem: finalize-output-fix-when-finalizer-outputp

(defthm finalize-output-fix-when-finalizer-outputp
  (implies (finalizer-outputp x)
           (equal (finalize-output-fix x) x)))

Function: finalize-output-equiv$inline

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

Theorem: finalize-output-equiv-is-an-equivalence

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

Theorem: finalize-output-equiv-implies-equal-finalize-output-fix-1

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

Theorem: finalize-output-fix-under-finalize-output-equiv

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

Theorem: equal-of-finalize-output-fix-1-forward-to-finalize-output-equiv

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

Theorem: equal-of-finalize-output-fix-2-forward-to-finalize-output-equiv

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

Theorem: finalize-output-equiv-of-finalize-output-fix-1-forward

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

Theorem: finalize-output-equiv-of-finalize-output-fix-2-forward

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