Fixing function for vl-sysfunname structures.
(vl-sysfunname-fix x) → new-x
Function:
(defun vl-sysfunname-fix$inline (x) (declare (xargs :guard (vl-sysfunname-p x))) (let ((__function__ 'vl-sysfunname-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((name (str-fix (cdr x)))) (cons :vl-sysfunname name)) :exec x)))
Theorem:
(defthm vl-sysfunname-p-of-vl-sysfunname-fix (b* ((new-x (vl-sysfunname-fix$inline x))) (vl-sysfunname-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm vl-sysfunname-fix-when-vl-sysfunname-p (implies (vl-sysfunname-p x) (equal (vl-sysfunname-fix x) x)))
Function:
(defun vl-sysfunname-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (vl-sysfunname-p acl2::x) (vl-sysfunname-p acl2::y)))) (equal (vl-sysfunname-fix acl2::x) (vl-sysfunname-fix acl2::y)))
Theorem:
(defthm vl-sysfunname-equiv-is-an-equivalence (and (booleanp (vl-sysfunname-equiv x y)) (vl-sysfunname-equiv x x) (implies (vl-sysfunname-equiv x y) (vl-sysfunname-equiv y x)) (implies (and (vl-sysfunname-equiv x y) (vl-sysfunname-equiv y z)) (vl-sysfunname-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm vl-sysfunname-equiv-implies-equal-vl-sysfunname-fix-1 (implies (vl-sysfunname-equiv acl2::x x-equiv) (equal (vl-sysfunname-fix acl2::x) (vl-sysfunname-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm vl-sysfunname-fix-under-vl-sysfunname-equiv (vl-sysfunname-equiv (vl-sysfunname-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-vl-sysfunname-fix-1-forward-to-vl-sysfunname-equiv (implies (equal (vl-sysfunname-fix acl2::x) acl2::y) (vl-sysfunname-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-vl-sysfunname-fix-2-forward-to-vl-sysfunname-equiv (implies (equal acl2::x (vl-sysfunname-fix acl2::y)) (vl-sysfunname-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm vl-sysfunname-equiv-of-vl-sysfunname-fix-1-forward (implies (vl-sysfunname-equiv (vl-sysfunname-fix acl2::x) acl2::y) (vl-sysfunname-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm vl-sysfunname-equiv-of-vl-sysfunname-fix-2-forward (implies (vl-sysfunname-equiv acl2::x (vl-sysfunname-fix acl2::y)) (vl-sysfunname-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)