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Scope-result

Scope-result-fix

Fixing function for scope-result structures.

Signature
(scope-result-fix acl2::x) → new-x
Arguments: acl2::x — Guard (scope-resultp acl2::x).
Returns: new-x — Type (scope-resultp new-x).

Definitions and Theorems

Function: scope-result-fix$inline

(defun scope-result-fix$inline (acl2::x)
  (declare (xargs :guard (scope-resultp acl2::x)))
  (let ((__function__ 'scope-result-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (scope-result-kind acl2::x)
           (:ok (b* ((get (scope-fix acl2::x))) get))
           (:err (b* ((get (error-fix acl2::x))) get)))
         :exec acl2::x)))

Theorem: scope-resultp-of-scope-result-fix

(defthm scope-resultp-of-scope-result-fix
  (b* ((new-x (scope-result-fix$inline acl2::x)))
    (scope-resultp new-x))
  :rule-classes :rewrite)

Theorem: scope-result-fix-when-scope-resultp

(defthm scope-result-fix-when-scope-resultp
  (implies (scope-resultp acl2::x)
           (equal (scope-result-fix acl2::x)
                  acl2::x)))

Function: scope-result-equiv$inline

(defun scope-result-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (scope-resultp acl2::x)
                              (scope-resultp acl2::y))))
  (equal (scope-result-fix acl2::x)
         (scope-result-fix acl2::y)))

Theorem: scope-result-equiv-is-an-equivalence

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

Theorem: scope-result-equiv-implies-equal-scope-result-fix-1

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

Theorem: scope-result-fix-under-scope-result-equiv

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

Theorem: equal-of-scope-result-fix-1-forward-to-scope-result-equiv

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

Theorem: equal-of-scope-result-fix-2-forward-to-scope-result-equiv

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

Theorem: scope-result-equiv-of-scope-result-fix-1-forward

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

Theorem: scope-result-equiv-of-scope-result-fix-2-forward

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

Theorem: scope-result-kind$inline-of-scope-result-fix-x

(defthm scope-result-kind$inline-of-scope-result-fix-x
  (equal (scope-result-kind$inline (scope-result-fix acl2::x))
         (scope-result-kind$inline acl2::x)))

Theorem: scope-result-kind$inline-scope-result-equiv-congruence-on-x

(defthm scope-result-kind$inline-scope-result-equiv-congruence-on-x
  (implies (scope-result-equiv acl2::x x-equiv)
           (equal (scope-result-kind$inline acl2::x)
                  (scope-result-kind$inline x-equiv)))
  :rule-classes :congruence)