Fixing function for stor-spec structures.
(stor-spec-fix x) → new-x
Function:
(defun stor-spec-fix$inline (x) (declare (xargs :guard (stor-specp x))) (let ((__function__ 'stor-spec-fix)) (declare (ignorable __function__)) (mbe :logic (case (stor-spec-kind x) (:typedef (cons :typedef (list))) (:extern (cons :extern (list))) (:static (cons :static (list))) (:threadloc (cons :threadloc (list))) (:auto (cons :auto (list))) (:register (cons :register (list)))) :exec x)))
Theorem:
(defthm stor-specp-of-stor-spec-fix (b* ((new-x (stor-spec-fix$inline x))) (stor-specp new-x)) :rule-classes :rewrite)
Theorem:
(defthm stor-spec-fix-when-stor-specp (implies (stor-specp x) (equal (stor-spec-fix x) x)))
Function:
(defun stor-spec-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (stor-specp acl2::x) (stor-specp acl2::y)))) (equal (stor-spec-fix acl2::x) (stor-spec-fix acl2::y)))
Theorem:
(defthm stor-spec-equiv-is-an-equivalence (and (booleanp (stor-spec-equiv x y)) (stor-spec-equiv x x) (implies (stor-spec-equiv x y) (stor-spec-equiv y x)) (implies (and (stor-spec-equiv x y) (stor-spec-equiv y z)) (stor-spec-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm stor-spec-equiv-implies-equal-stor-spec-fix-1 (implies (stor-spec-equiv acl2::x x-equiv) (equal (stor-spec-fix acl2::x) (stor-spec-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm stor-spec-fix-under-stor-spec-equiv (stor-spec-equiv (stor-spec-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-stor-spec-fix-1-forward-to-stor-spec-equiv (implies (equal (stor-spec-fix acl2::x) acl2::y) (stor-spec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-stor-spec-fix-2-forward-to-stor-spec-equiv (implies (equal acl2::x (stor-spec-fix acl2::y)) (stor-spec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm stor-spec-equiv-of-stor-spec-fix-1-forward (implies (stor-spec-equiv (stor-spec-fix acl2::x) acl2::y) (stor-spec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm stor-spec-equiv-of-stor-spec-fix-2-forward (implies (stor-spec-equiv acl2::x (stor-spec-fix acl2::y)) (stor-spec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm stor-spec-kind$inline-of-stor-spec-fix-x (equal (stor-spec-kind$inline (stor-spec-fix x)) (stor-spec-kind$inline x)))
Theorem:
(defthm stor-spec-kind$inline-stor-spec-equiv-congruence-on-x (implies (stor-spec-equiv x x-equiv) (equal (stor-spec-kind$inline x) (stor-spec-kind$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm consp-of-stor-spec-fix (consp (stor-spec-fix x)) :rule-classes :type-prescription)