Fixing function for unicode-input-char structures.
(unicode-input-char-fix x) → new-x
Function:
(defun unicode-input-char-fix$inline (x) (declare (xargs :guard (unicode-input-char-p x))) (let ((__function__ 'unicode-input-char-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((unicode (unicode-fix (std::da-nth 0 (cdr x)))) (umarker (nfix (std::da-nth 1 (cdr x))))) (cons :unicode-input-char (list unicode umarker))) :exec x)))
Theorem:
(defthm unicode-input-char-p-of-unicode-input-char-fix (b* ((new-x (unicode-input-char-fix$inline x))) (unicode-input-char-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm unicode-input-char-fix-when-unicode-input-char-p (implies (unicode-input-char-p x) (equal (unicode-input-char-fix x) x)))
Function:
(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:
(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:
(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:
(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:
(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:
(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:
(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:
(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)