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• Value-list-result

Value-list-result-fix

Fixing function for value-list-result structures.

Signature

(value-list-result-fix acl2::x) → new-x

Arguments

acl2::x — Guard (value-list-resultp acl2::x).

Returns

new-x — Type (value-list-resultp new-x).

Definitions and Theorems

Function: value-list-result-fix$inline

(defun value-list-result-fix$inline (acl2::x)
  (declare (xargs :guard (value-list-resultp acl2::x)))
  (mbe :logic
       (case (value-list-result-kind acl2::x)
         (:ok (b* ((get (value-list-fix acl2::x)))
                get))
         (:err (b* ((get (error-fix acl2::x))) get)))
       :exec acl2::x))

Theorem: value-list-resultp-of-value-list-result-fix

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

Theorem: value-list-result-fix-when-value-list-resultp

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

Function: value-list-result-equiv$inline

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

Theorem: value-list-result-equiv-is-an-equivalence

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

Theorem: value-list-result-equiv-implies-equal-value-list-result-fix-1

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

Theorem: value-list-result-fix-under-value-list-result-equiv

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

Theorem: equal-of-value-list-result-fix-1-forward-to-value-list-result-equiv

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

Theorem: equal-of-value-list-result-fix-2-forward-to-value-list-result-equiv

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

Theorem: value-list-result-equiv-of-value-list-result-fix-1-forward

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

Theorem: value-list-result-equiv-of-value-list-result-fix-2-forward

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

Theorem: value-list-result-kind$inline-of-value-list-result-fix-x

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

Theorem: value-list-result-kind$inline-value-list-result-equiv-congruence-on-x

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

Theorem: value-list-result-fix$inline-of-value-list-result-fix-x

(defthm value-list-result-fix$inline-of-value-list-result-fix-x
 (equal
      (value-list-result-fix$inline (value-list-result-fix acl2::x))
      (value-list-result-fix$inline acl2::x)))

Theorem: value-list-result-fix$inline-value-list-result-equiv-congruence-on-x

(defthm
 value-list-result-fix$inline-value-list-result-equiv-congruence-on-x
 (implies (value-list-result-equiv acl2::x x-equiv)
          (equal (value-list-result-fix$inline acl2::x)
                 (value-list-result-fix$inline x-equiv)))
 :rule-classes :congruence)