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Vardecl-result

Vardecl-result-fix

Fixing function for vardecl-result structures.

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

Definitions and Theorems

Function: vardecl-result-fix$inline

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

Theorem: vardecl-resultp-of-vardecl-result-fix

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

Theorem: vardecl-result-fix-when-vardecl-resultp

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

Function: vardecl-result-equiv$inline

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

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

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

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

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

Theorem: vardecl-result-fix-under-vardecl-result-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-vardecl-result-fix

(defthm consp-of-vardecl-result-fix
  (consp (vardecl-result-fix acl2::x))
  :rule-classes :type-prescription)