Fixing function for univ-char-name structures.
(univ-char-name-fix x) → new-x
Function:
(defun univ-char-name-fix$inline (x) (declare (xargs :guard (univ-char-name-p x))) (let ((__function__ 'univ-char-name-fix)) (declare (ignorable __function__)) (mbe :logic (case (univ-char-name-kind x) (:locase-u (b* ((quad (hex-quad-fix (std::da-nth 0 (cdr x))))) (cons :locase-u (list quad)))) (:upcase-u (b* ((quad1 (hex-quad-fix (std::da-nth 0 (cdr x)))) (quad2 (hex-quad-fix (std::da-nth 1 (cdr x))))) (cons :upcase-u (list quad1 quad2))))) :exec x)))
Theorem:
(defthm univ-char-name-p-of-univ-char-name-fix (b* ((new-x (univ-char-name-fix$inline x))) (univ-char-name-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm univ-char-name-fix-when-univ-char-name-p (implies (univ-char-name-p x) (equal (univ-char-name-fix x) x)))
Function:
(defun univ-char-name-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (univ-char-name-p acl2::x) (univ-char-name-p acl2::y)))) (equal (univ-char-name-fix acl2::x) (univ-char-name-fix acl2::y)))
Theorem:
(defthm univ-char-name-equiv-is-an-equivalence (and (booleanp (univ-char-name-equiv x y)) (univ-char-name-equiv x x) (implies (univ-char-name-equiv x y) (univ-char-name-equiv y x)) (implies (and (univ-char-name-equiv x y) (univ-char-name-equiv y z)) (univ-char-name-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm univ-char-name-equiv-implies-equal-univ-char-name-fix-1 (implies (univ-char-name-equiv acl2::x x-equiv) (equal (univ-char-name-fix acl2::x) (univ-char-name-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm univ-char-name-fix-under-univ-char-name-equiv (univ-char-name-equiv (univ-char-name-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-univ-char-name-fix-1-forward-to-univ-char-name-equiv (implies (equal (univ-char-name-fix acl2::x) acl2::y) (univ-char-name-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-univ-char-name-fix-2-forward-to-univ-char-name-equiv (implies (equal acl2::x (univ-char-name-fix acl2::y)) (univ-char-name-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm univ-char-name-equiv-of-univ-char-name-fix-1-forward (implies (univ-char-name-equiv (univ-char-name-fix acl2::x) acl2::y) (univ-char-name-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm univ-char-name-equiv-of-univ-char-name-fix-2-forward (implies (univ-char-name-equiv acl2::x (univ-char-name-fix acl2::y)) (univ-char-name-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm univ-char-name-kind$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:
(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:
(defthm consp-of-univ-char-name-fix (consp (univ-char-name-fix x)) :rule-classes :type-prescription)