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