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• Unicode-input-char

Unicode-input-char-fix

Fixing function for unicode-input-char structures.

Signature

(unicode-input-char-fix x) → new-x

Arguments

x — Guard (unicode-input-char-p x).

Returns

new-x — Type (unicode-input-char-p new-x).

Definitions and Theorems

Function: unicode-input-char-fix$inline

(defun unicode-input-char-fix$inline (x)
  (declare (xargs :guard (unicode-input-char-p x)))
  (let ((__function__ 'unicode-input-char-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((unicode (unicode-fix (std::da-nth 0 (cdr x))))
              (umarker (nfix (std::da-nth 1 (cdr x)))))
           (cons :unicode-input-char (list unicode umarker)))
         :exec x)))

Theorem: unicode-input-char-p-of-unicode-input-char-fix

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

Theorem: unicode-input-char-fix-when-unicode-input-char-p

(defthm unicode-input-char-fix-when-unicode-input-char-p
  (implies (unicode-input-char-p x)
           (equal (unicode-input-char-fix x) x)))

Function: unicode-input-char-equiv$inline

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

Theorem: unicode-input-char-equiv-is-an-equivalence

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

Theorem: unicode-input-char-equiv-implies-equal-unicode-input-char-fix-1

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

Theorem: unicode-input-char-fix-under-unicode-input-char-equiv

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

Theorem: equal-of-unicode-input-char-fix-1-forward-to-unicode-input-char-equiv

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

Theorem: equal-of-unicode-input-char-fix-2-forward-to-unicode-input-char-equiv

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

Theorem: unicode-input-char-equiv-of-unicode-input-char-fix-1-forward

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

Theorem: unicode-input-char-equiv-of-unicode-input-char-fix-2-forward

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