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Character-list-result

Character-list-result-fix

Fixing function for character-list-result structures.

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

Definitions and Theorems

Function: character-list-result-fix$inline

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

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

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

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

(defthm character-list-result-fix-when-character-list-resultp
  (implies (character-list-resultp x)
           (equal (character-list-result-fix x)
                  x)))

Function: character-list-result-equiv$inline

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm
   character-list-result-kind$inline-of-character-list-result-fix-x
 (equal
   (character-list-result-kind$inline (character-list-result-fix x))
   (character-list-result-kind$inline x)))

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

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