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Char-value

Char-value-fix

Fixing function for char-value structures.

Signature
(char-value-fix x) → new-x
Arguments: x — Guard (char-valuep x).
Returns: new-x — Type (char-valuep new-x).

Definitions and Theorems

Function: char-value-fix$inline

(defun char-value-fix$inline (x)
  (declare (xargs :guard (char-valuep x)))
  (let ((__function__ 'char-value-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((nat (acl2::ubyte16-fix (std::da-nth 0 (cdr x)))))
           (cons :char (list nat)))
         :exec x)))

Theorem: char-valuep-of-char-value-fix

(defthm char-valuep-of-char-value-fix
  (b* ((new-x (char-value-fix$inline x)))
    (char-valuep new-x))
  :rule-classes :rewrite)

Theorem: char-value-fix-when-char-valuep

(defthm char-value-fix-when-char-valuep
  (implies (char-valuep x)
           (equal (char-value-fix x) x)))

Function: char-value-equiv$inline

(defun char-value-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (char-valuep acl2::x)
                              (char-valuep acl2::y))))
  (equal (char-value-fix acl2::x)
         (char-value-fix acl2::y)))

Theorem: char-value-equiv-is-an-equivalence

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

Theorem: char-value-equiv-implies-equal-char-value-fix-1

(defthm char-value-equiv-implies-equal-char-value-fix-1
  (implies (char-value-equiv acl2::x x-equiv)
           (equal (char-value-fix acl2::x)
                  (char-value-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: char-value-fix-under-char-value-equiv

(defthm char-value-fix-under-char-value-equiv
  (char-value-equiv (char-value-fix acl2::x)
                    acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-char-value-fix-1-forward-to-char-value-equiv

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

Theorem: equal-of-char-value-fix-2-forward-to-char-value-equiv

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

Theorem: char-value-equiv-of-char-value-fix-1-forward

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

Theorem: char-value-equiv-of-char-value-fix-2-forward

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