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