Fixing function for vars+modes-result structures.
(vars+modes-result-fix acl2::x) → new-x
Function:
(defun vars+modes-result-fix$inline (acl2::x) (declare (xargs :guard (vars+modes-resultp acl2::x))) (let ((__function__ 'vars+modes-result-fix)) (declare (ignorable __function__)) (mbe :logic (case (vars+modes-result-kind acl2::x) (:ok (b* ((get (vars+modes-fix acl2::x))) get)) (:err (b* ((get (fty::reserr-fix acl2::x))) get))) :exec acl2::x)))
Theorem:
(defthm vars+modes-resultp-of-vars+modes-result-fix (b* ((new-x (vars+modes-result-fix$inline acl2::x))) (vars+modes-resultp new-x)) :rule-classes :rewrite)
Theorem:
(defthm vars+modes-result-fix-when-vars+modes-resultp (implies (vars+modes-resultp acl2::x) (equal (vars+modes-result-fix acl2::x) acl2::x)))
Function:
(defun vars+modes-result-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (vars+modes-resultp acl2::x) (vars+modes-resultp acl2::y)))) (equal (vars+modes-result-fix acl2::x) (vars+modes-result-fix acl2::y)))
Theorem:
(defthm vars+modes-result-equiv-is-an-equivalence (and (booleanp (vars+modes-result-equiv x y)) (vars+modes-result-equiv x x) (implies (vars+modes-result-equiv x y) (vars+modes-result-equiv y x)) (implies (and (vars+modes-result-equiv x y) (vars+modes-result-equiv y z)) (vars+modes-result-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm vars+modes-result-equiv-implies-equal-vars+modes-result-fix-1 (implies (vars+modes-result-equiv acl2::x x-equiv) (equal (vars+modes-result-fix acl2::x) (vars+modes-result-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm vars+modes-result-fix-under-vars+modes-result-equiv (vars+modes-result-equiv (vars+modes-result-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-vars+modes-result-fix-1-forward-to-vars+modes-result-equiv (implies (equal (vars+modes-result-fix acl2::x) acl2::y) (vars+modes-result-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-vars+modes-result-fix-2-forward-to-vars+modes-result-equiv (implies (equal acl2::x (vars+modes-result-fix acl2::y)) (vars+modes-result-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm vars+modes-result-equiv-of-vars+modes-result-fix-1-forward (implies (vars+modes-result-equiv (vars+modes-result-fix acl2::x) acl2::y) (vars+modes-result-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm vars+modes-result-equiv-of-vars+modes-result-fix-2-forward (implies (vars+modes-result-equiv acl2::x (vars+modes-result-fix acl2::y)) (vars+modes-result-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm vars+modes-result-kind$inline-of-vars+modes-result-fix-x (equal (vars+modes-result-kind$inline (vars+modes-result-fix acl2::x)) (vars+modes-result-kind$inline acl2::x)))
Theorem:
(defthm vars+modes-result-kind$inline-vars+modes-result-equiv-congruence-on-x (implies (vars+modes-result-equiv acl2::x x-equiv) (equal (vars+modes-result-kind$inline acl2::x) (vars+modes-result-kind$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm consp-of-vars+modes-result-fix (consp (vars+modes-result-fix acl2::x)) :rule-classes :type-prescription)