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Tree-list-tuple10-result

Tree-list-tuple10-result-fix

Fixing function for tree-list-tuple10-result structures.

Signature
(tree-list-tuple10-result-fix acl2::x) → new-x
Arguments: acl2::x — Guard (tree-list-tuple10-resultp acl2::x).
Returns: new-x — Type (tree-list-tuple10-resultp new-x).

Definitions and Theorems

Function: tree-list-tuple10-result-fix$inline

(defun tree-list-tuple10-result-fix$inline (acl2::x)
  (declare (xargs :guard (tree-list-tuple10-resultp acl2::x)))
  (let ((__function__ 'tree-list-tuple10-result-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (case (tree-list-tuple10-result-kind acl2::x)
           (:ok (b* ((get (tree-list-tuple10-fix acl2::x)))
                  get))
           (:err (b* ((get (fty::reserr-fix acl2::x)))
                   get)))
         :exec acl2::x)))

Theorem: tree-list-tuple10-resultp-of-tree-list-tuple10-result-fix

(defthm tree-list-tuple10-resultp-of-tree-list-tuple10-result-fix
  (b* ((new-x (tree-list-tuple10-result-fix$inline acl2::x)))
    (tree-list-tuple10-resultp new-x))
  :rule-classes :rewrite)

Theorem: tree-list-tuple10-result-fix-when-tree-list-tuple10-resultp

(defthm tree-list-tuple10-result-fix-when-tree-list-tuple10-resultp
  (implies (tree-list-tuple10-resultp acl2::x)
           (equal (tree-list-tuple10-result-fix acl2::x)
                  acl2::x)))

Function: tree-list-tuple10-result-equiv$inline

(defun tree-list-tuple10-result-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (tree-list-tuple10-resultp acl2::x)
                              (tree-list-tuple10-resultp acl2::y))))
  (equal (tree-list-tuple10-result-fix acl2::x)
         (tree-list-tuple10-result-fix acl2::y)))

Theorem: tree-list-tuple10-result-equiv-is-an-equivalence

(defthm tree-list-tuple10-result-equiv-is-an-equivalence
  (and (booleanp (tree-list-tuple10-result-equiv x y))
       (tree-list-tuple10-result-equiv x x)
       (implies (tree-list-tuple10-result-equiv x y)
                (tree-list-tuple10-result-equiv y x))
       (implies (and (tree-list-tuple10-result-equiv x y)
                     (tree-list-tuple10-result-equiv y z))
                (tree-list-tuple10-result-equiv x z)))
  :rule-classes (:equivalence))

Theorem: tree-list-tuple10-result-equiv-implies-equal-tree-list-tuple10-result-fix-1

(defthm
 tree-list-tuple10-result-equiv-implies-equal-tree-list-tuple10-result-fix-1
 (implies (tree-list-tuple10-result-equiv acl2::x x-equiv)
          (equal (tree-list-tuple10-result-fix acl2::x)
                 (tree-list-tuple10-result-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: tree-list-tuple10-result-fix-under-tree-list-tuple10-result-equiv

(defthm
  tree-list-tuple10-result-fix-under-tree-list-tuple10-result-equiv
  (tree-list-tuple10-result-equiv
       (tree-list-tuple10-result-fix acl2::x)
       acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-tree-list-tuple10-result-fix-1-forward-to-tree-list-tuple10-result-equiv

(defthm
 equal-of-tree-list-tuple10-result-fix-1-forward-to-tree-list-tuple10-result-equiv
 (implies (equal (tree-list-tuple10-result-fix acl2::x)
                 acl2::y)
          (tree-list-tuple10-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-tree-list-tuple10-result-fix-2-forward-to-tree-list-tuple10-result-equiv

(defthm
 equal-of-tree-list-tuple10-result-fix-2-forward-to-tree-list-tuple10-result-equiv
 (implies (equal acl2::x
                 (tree-list-tuple10-result-fix acl2::y))
          (tree-list-tuple10-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: tree-list-tuple10-result-equiv-of-tree-list-tuple10-result-fix-1-forward

(defthm
 tree-list-tuple10-result-equiv-of-tree-list-tuple10-result-fix-1-forward
 (implies (tree-list-tuple10-result-equiv
               (tree-list-tuple10-result-fix acl2::x)
               acl2::y)
          (tree-list-tuple10-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: tree-list-tuple10-result-equiv-of-tree-list-tuple10-result-fix-2-forward

(defthm
 tree-list-tuple10-result-equiv-of-tree-list-tuple10-result-fix-2-forward
 (implies (tree-list-tuple10-result-equiv
               acl2::x
               (tree-list-tuple10-result-fix acl2::y))
          (tree-list-tuple10-result-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: tree-list-tuple10-result-kind$inline-of-tree-list-tuple10-result-fix-x

(defthm
 tree-list-tuple10-result-kind$inline-of-tree-list-tuple10-result-fix-x
 (equal (tree-list-tuple10-result-kind$inline
             (tree-list-tuple10-result-fix acl2::x))
        (tree-list-tuple10-result-kind$inline acl2::x)))

Theorem: tree-list-tuple10-result-kind$inline-tree-list-tuple10-result-equiv-congruence-on-x

(defthm
 tree-list-tuple10-result-kind$inline-tree-list-tuple10-result-equiv-congruence-on-x
 (implies (tree-list-tuple10-result-equiv acl2::x x-equiv)
          (equal (tree-list-tuple10-result-kind$inline acl2::x)
                 (tree-list-tuple10-result-kind$inline x-equiv)))
 :rule-classes :congruence)

Theorem: consp-of-tree-list-tuple10-result-fix

(defthm consp-of-tree-list-tuple10-result-fix
  (consp (tree-list-tuple10-result-fix acl2::x))
  :rule-classes :type-prescription)