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• Natoption/natoptionlist-result

Natoption/natoptionlist-result-fix

Fixing function for natoption/natoptionlist-result structures.

Signature

(natoption/natoptionlist-result-fix x) → new-x

Arguments

x — Guard (natoption/natoptionlist-resultp x).

Returns

new-x — Type (natoption/natoptionlist-resultp new-x).

Definitions and Theorems

Function: natoption/natoptionlist-result-fix$inline

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

Theorem: natoption/natoptionlist-resultp-of-natoption/natoptionlist-result-fix

(defthm
 natoption/natoptionlist-resultp-of-natoption/natoptionlist-result-fix
 (b* ((new-x (natoption/natoptionlist-result-fix$inline x)))
   (natoption/natoptionlist-resultp new-x))
 :rule-classes :rewrite)

Theorem: natoption/natoptionlist-result-fix-when-natoption/natoptionlist-resultp

(defthm
 natoption/natoptionlist-result-fix-when-natoption/natoptionlist-resultp
 (implies (natoption/natoptionlist-resultp x)
          (equal (natoption/natoptionlist-result-fix x)
                 x)))

Function: natoption/natoptionlist-result-equiv$inline

(defun natoption/natoptionlist-result-equiv$inline (x y)
  (declare (xargs :guard (and (natoption/natoptionlist-resultp x)
                              (natoption/natoptionlist-resultp y))))
  (equal (natoption/natoptionlist-result-fix x)
         (natoption/natoptionlist-result-fix y)))

Theorem: natoption/natoptionlist-result-equiv-is-an-equivalence

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

Theorem: natoption/natoptionlist-result-equiv-implies-equal-natoption/natoptionlist-result-fix-1

(defthm
 natoption/natoptionlist-result-equiv-implies-equal-natoption/natoptionlist-result-fix-1
 (implies (natoption/natoptionlist-result-equiv x x-equiv)
          (equal (natoption/natoptionlist-result-fix x)
                 (natoption/natoptionlist-result-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: natoption/natoptionlist-result-fix-under-natoption/natoptionlist-result-equiv

(defthm
 natoption/natoptionlist-result-fix-under-natoption/natoptionlist-result-equiv
 (natoption/natoptionlist-result-equiv
      (natoption/natoptionlist-result-fix x)
      x)
 :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-natoption/natoptionlist-result-fix-1-forward-to-natoption/natoptionlist-result-equiv

(defthm
 equal-of-natoption/natoptionlist-result-fix-1-forward-to-natoption/natoptionlist-result-equiv
 (implies (equal (natoption/natoptionlist-result-fix x)
                 y)
          (natoption/natoptionlist-result-equiv x y))
 :rule-classes :forward-chaining)

Theorem: equal-of-natoption/natoptionlist-result-fix-2-forward-to-natoption/natoptionlist-result-equiv

(defthm
 equal-of-natoption/natoptionlist-result-fix-2-forward-to-natoption/natoptionlist-result-equiv
 (implies (equal x
                 (natoption/natoptionlist-result-fix y))
          (natoption/natoptionlist-result-equiv x y))
 :rule-classes :forward-chaining)

Theorem: natoption/natoptionlist-result-equiv-of-natoption/natoptionlist-result-fix-1-forward

(defthm
 natoption/natoptionlist-result-equiv-of-natoption/natoptionlist-result-fix-1-forward
 (implies (natoption/natoptionlist-result-equiv
               (natoption/natoptionlist-result-fix x)
               y)
          (natoption/natoptionlist-result-equiv x y))
 :rule-classes :forward-chaining)

Theorem: natoption/natoptionlist-result-equiv-of-natoption/natoptionlist-result-fix-2-forward

(defthm
 natoption/natoptionlist-result-equiv-of-natoption/natoptionlist-result-fix-2-forward
 (implies (natoption/natoptionlist-result-equiv
               x
               (natoption/natoptionlist-result-fix y))
          (natoption/natoptionlist-result-equiv x y))
 :rule-classes :forward-chaining)

Theorem: natoption/natoptionlist-result-kind$inline-of-natoption/natoptionlist-result-fix-x

(defthm
 natoption/natoptionlist-result-kind$inline-of-natoption/natoptionlist-result-fix-x
 (equal (natoption/natoptionlist-result-kind$inline
             (natoption/natoptionlist-result-fix x))
        (natoption/natoptionlist-result-kind$inline x)))

Theorem: natoption/natoptionlist-result-kind$inline-natoption/natoptionlist-result-equiv-congruence-on-x

(defthm
 natoption/natoptionlist-result-kind$inline-natoption/natoptionlist-result-equiv-congruence-on-x
 (implies
      (natoption/natoptionlist-result-equiv x x-equiv)
      (equal (natoption/natoptionlist-result-kind$inline x)
             (natoption/natoptionlist-result-kind$inline x-equiv)))
 :rule-classes :congruence)

Theorem: consp-of-natoption/natoptionlist-result-fix

(defthm consp-of-natoption/natoptionlist-result-fix
  (consp (natoption/natoptionlist-result-fix x))
  :rule-classes :type-prescription)