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Char-val

Char-val-fix

Fixing function for char-val structures.

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

Definitions and Theorems

Function: char-val-fix$inline

(defun char-val-fix$inline (x)
 (declare (xargs :guard (char-val-p x)))
 (let ((__function__ 'char-val-fix))
  (declare (ignorable __function__))
  (mbe
      :logic
      (case (char-val-kind x)
        (:sensitive (b* ((get (str-fix (std::da-nth 0 (cdr x)))))
                      (cons :sensitive (list get))))
        (:insensitive
             (b* ((iprefix (acl2::bool-fix (std::da-nth 0 (cdr x))))
                  (get (str-fix (std::da-nth 1 (cdr x)))))
               (cons :insensitive (list iprefix get)))))
      :exec x)))

Theorem: char-val-p-of-char-val-fix

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

Theorem: char-val-fix-when-char-val-p

(defthm char-val-fix-when-char-val-p
  (implies (char-val-p x)
           (equal (char-val-fix x) x)))

Function: char-val-equiv$inline

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

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

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

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

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

Theorem: char-val-fix-under-char-val-equiv

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

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

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

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

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

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

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

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

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

Theorem: char-val-kind$inline-of-char-val-fix-x

(defthm char-val-kind$inline-of-char-val-fix-x
  (equal (char-val-kind$inline (char-val-fix x))
         (char-val-kind$inline x)))

Theorem: char-val-kind$inline-char-val-equiv-congruence-on-x

(defthm char-val-kind$inline-char-val-equiv-congruence-on-x
  (implies (char-val-equiv x x-equiv)
           (equal (char-val-kind$inline x)
                  (char-val-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-char-val-fix

(defthm consp-of-char-val-fix
  (consp (char-val-fix x))
  :rule-classes :type-prescription)