Fixing function for tag-info structures.
Function:
(defun tag-info-fix$inline (x) (declare (xargs :guard (tag-infop x))) (let ((__function__ 'tag-info-fix)) (declare (ignorable __function__)) (mbe :logic (case (tag-info-kind x) (:struct (b* ((members (member-type-list-fix (std::da-nth 0 (cdr x))))) (cons :struct (list members)))) (:union (cons :union (list))) (:enum (cons :enum (list)))) :exec x)))
Theorem:
(defthm tag-infop-of-tag-info-fix (b* ((new-x (tag-info-fix$inline x))) (tag-infop new-x)) :rule-classes :rewrite)
Theorem:
(defthm tag-info-fix-when-tag-infop (implies (tag-infop x) (equal (tag-info-fix x) x)))
Function:
(defun tag-info-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (tag-infop acl2::x) (tag-infop acl2::y)))) (equal (tag-info-fix acl2::x) (tag-info-fix acl2::y)))
Theorem:
(defthm tag-info-equiv-is-an-equivalence (and (booleanp (tag-info-equiv x y)) (tag-info-equiv x x) (implies (tag-info-equiv x y) (tag-info-equiv y x)) (implies (and (tag-info-equiv x y) (tag-info-equiv y z)) (tag-info-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm tag-info-equiv-implies-equal-tag-info-fix-1 (implies (tag-info-equiv acl2::x x-equiv) (equal (tag-info-fix acl2::x) (tag-info-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm tag-info-fix-under-tag-info-equiv (tag-info-equiv (tag-info-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-tag-info-fix-1-forward-to-tag-info-equiv (implies (equal (tag-info-fix acl2::x) acl2::y) (tag-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-tag-info-fix-2-forward-to-tag-info-equiv (implies (equal acl2::x (tag-info-fix acl2::y)) (tag-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm tag-info-equiv-of-tag-info-fix-1-forward (implies (tag-info-equiv (tag-info-fix acl2::x) acl2::y) (tag-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm tag-info-equiv-of-tag-info-fix-2-forward (implies (tag-info-equiv acl2::x (tag-info-fix acl2::y)) (tag-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm tag-info-kind$inline-of-tag-info-fix-x (equal (tag-info-kind$inline (tag-info-fix x)) (tag-info-kind$inline x)))
Theorem:
(defthm tag-info-kind$inline-tag-info-equiv-congruence-on-x (implies (tag-info-equiv x x-equiv) (equal (tag-info-kind$inline x) (tag-info-kind$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm consp-of-tag-info-fix (consp (tag-info-fix x)) :rule-classes :type-prescription)