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Funparam-list-result

Funparam-list-result-fix

Fixing function for funparam-list-result structures.

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

Definitions and Theorems

Function: funparam-list-result-fix$inline

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

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

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

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

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

Function: funparam-list-result-equiv$inline

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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