Fixing function for vl-coredatatype-info structures.
(vl-coredatatype-info-fix x) → new-x
Function:
(defun vl-coredatatype-info-fix$inline (x) (declare (xargs :guard (vl-coredatatype-info-p x))) (let ((__function__ 'vl-coredatatype-info-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((coretypename (vl-coretypename-fix (std::prod-car (std::prod-car x)))) (keyword (acl2::symbol-fix (std::prod-car (std::prod-cdr (std::prod-car x))))) (default-signedp (acl2::bool-fix (std::prod-cdr (std::prod-cdr (std::prod-car x))))) (takes-signingp (acl2::bool-fix (std::prod-car (std::prod-car (std::prod-cdr x))))) (takes-dimensionsp (acl2::bool-fix (std::prod-cdr (std::prod-car (std::prod-cdr x))))) (4valuedp (acl2::bool-fix (std::prod-car (std::prod-cdr (std::prod-cdr x))))) (size (acl2::maybe-posp-fix (std::prod-cdr (std::prod-cdr (std::prod-cdr x)))))) (std::prod-cons (std::prod-cons coretypename (std::prod-cons keyword default-signedp)) (std::prod-cons (std::prod-cons takes-signingp takes-dimensionsp) (std::prod-cons 4valuedp size)))) :exec x)))
Theorem:
(defthm vl-coredatatype-info-p-of-vl-coredatatype-info-fix (b* ((new-x (vl-coredatatype-info-fix$inline x))) (vl-coredatatype-info-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm vl-coredatatype-info-fix-when-vl-coredatatype-info-p (implies (vl-coredatatype-info-p x) (equal (vl-coredatatype-info-fix x) x)))
Function:
(defun vl-coredatatype-info-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (vl-coredatatype-info-p acl2::x) (vl-coredatatype-info-p acl2::y)))) (equal (vl-coredatatype-info-fix acl2::x) (vl-coredatatype-info-fix acl2::y)))
Theorem:
(defthm vl-coredatatype-info-equiv-is-an-equivalence (and (booleanp (vl-coredatatype-info-equiv x y)) (vl-coredatatype-info-equiv x x) (implies (vl-coredatatype-info-equiv x y) (vl-coredatatype-info-equiv y x)) (implies (and (vl-coredatatype-info-equiv x y) (vl-coredatatype-info-equiv y z)) (vl-coredatatype-info-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm vl-coredatatype-info-equiv-implies-equal-vl-coredatatype-info-fix-1 (implies (vl-coredatatype-info-equiv acl2::x x-equiv) (equal (vl-coredatatype-info-fix acl2::x) (vl-coredatatype-info-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm vl-coredatatype-info-fix-under-vl-coredatatype-info-equiv (vl-coredatatype-info-equiv (vl-coredatatype-info-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-vl-coredatatype-info-fix-1-forward-to-vl-coredatatype-info-equiv (implies (equal (vl-coredatatype-info-fix acl2::x) acl2::y) (vl-coredatatype-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-vl-coredatatype-info-fix-2-forward-to-vl-coredatatype-info-equiv (implies (equal acl2::x (vl-coredatatype-info-fix acl2::y)) (vl-coredatatype-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm vl-coredatatype-info-equiv-of-vl-coredatatype-info-fix-1-forward (implies (vl-coredatatype-info-equiv (vl-coredatatype-info-fix acl2::x) acl2::y) (vl-coredatatype-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm vl-coredatatype-info-equiv-of-vl-coredatatype-info-fix-2-forward (implies (vl-coredatatype-info-equiv acl2::x (vl-coredatatype-info-fix acl2::y)) (vl-coredatatype-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)