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• Univ-char-name

Univ-char-name-fix

Fixing function for univ-char-name structures.

Signature

(univ-char-name-fix x) → new-x

Arguments

x — Guard (univ-char-name-p x).

Returns

new-x — Type (univ-char-name-p new-x).

Definitions and Theorems

Function: univ-char-name-fix$inline

(defun univ-char-name-fix$inline (x)
 (declare (xargs :guard (univ-char-name-p x)))
 (let ((__function__ 'univ-char-name-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (univ-char-name-kind x)
     (:locase-u (b* ((quad (hex-quad-fix (std::da-nth 0 (cdr x)))))
                  (cons :locase-u (list quad))))
     (:upcase-u (b* ((quad1 (hex-quad-fix (std::da-nth 0 (cdr x))))
                     (quad2 (hex-quad-fix (std::da-nth 1 (cdr x)))))
                  (cons :upcase-u (list quad1 quad2)))))
   :exec x)))

Theorem: univ-char-name-p-of-univ-char-name-fix

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

Theorem: univ-char-name-fix-when-univ-char-name-p

(defthm univ-char-name-fix-when-univ-char-name-p
  (implies (univ-char-name-p x)
           (equal (univ-char-name-fix x) x)))

Function: univ-char-name-equiv$inline

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

Theorem: univ-char-name-equiv-is-an-equivalence

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

Theorem: univ-char-name-equiv-implies-equal-univ-char-name-fix-1

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

Theorem: univ-char-name-fix-under-univ-char-name-equiv

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

Theorem: equal-of-univ-char-name-fix-1-forward-to-univ-char-name-equiv

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

Theorem: equal-of-univ-char-name-fix-2-forward-to-univ-char-name-equiv

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

Theorem: univ-char-name-equiv-of-univ-char-name-fix-1-forward

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

Theorem: univ-char-name-equiv-of-univ-char-name-fix-2-forward

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

Theorem: univ-char-name-kind$inline-of-univ-char-name-fix-x

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

Theorem: univ-char-name-kind$inline-univ-char-name-equiv-congruence-on-x

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

Theorem: consp-of-univ-char-name-fix

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