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