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Programid-result

Programid-result-fix

Fixing function for programid-result structures.

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

Definitions and Theorems

Function: programid-result-fix$inline

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

Theorem: programid-resultp-of-programid-result-fix

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

Theorem: programid-result-fix-when-programid-resultp

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

Function: programid-result-equiv$inline

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

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

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

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

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

Theorem: programid-result-fix-under-programid-result-equiv

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

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

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

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

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

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

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

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

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

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

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

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

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

Theorem: consp-of-programid-result-fix

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