Recognizer for occ-name-alist.
(occ-name-alist-p x) → *
Function:
(defun occ-name-alist-p (x) (declare (xargs :guard t)) (let ((acl2::__function__ 'occ-name-alist-p)) (declare (ignorable acl2::__function__)) (if (atom x) t (and (consp (car x)) (occ-name-p (caar x)) (occ-name-list-p (cdar x)) (occ-name-alist-p (cdr x))))))
Theorem:
(defthm occ-name-alist-p-of-butlast (implies (occ-name-alist-p (double-rewrite acl2::x)) (occ-name-alist-p (butlast acl2::x acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-alist-p-of-repeat (iff (occ-name-alist-p (repeat acl2::n acl2::x)) (or (and (consp acl2::x) (occ-name-p (car acl2::x)) (occ-name-list-p (cdr acl2::x))) (zp acl2::n))) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-alist-p-of-rev (equal (occ-name-alist-p (rev acl2::x)) (occ-name-alist-p (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-alist-p-of-list-fix (equal (occ-name-alist-p (list-fix acl2::x)) (occ-name-alist-p acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-alist-p-of-append (equal (occ-name-alist-p (append acl2::a acl2::b)) (and (occ-name-alist-p acl2::a) (occ-name-alist-p acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-alist-p-when-not-consp (implies (not (consp acl2::x)) (occ-name-alist-p acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-alist-p-of-cdr-when-occ-name-alist-p (implies (occ-name-alist-p (double-rewrite acl2::x)) (occ-name-alist-p (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-alist-p-of-cons (equal (occ-name-alist-p (cons acl2::a acl2::x)) (and (and (consp acl2::a) (occ-name-p (car acl2::a)) (occ-name-list-p (cdr acl2::a))) (occ-name-alist-p acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-alist-p-of-fast-alist-clean (implies (occ-name-alist-p acl2::x) (occ-name-alist-p (fast-alist-clean acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-alist-p-of-hons-shrink-alist (implies (and (occ-name-alist-p acl2::x) (occ-name-alist-p acl2::y)) (occ-name-alist-p (hons-shrink-alist acl2::x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-alist-p-of-hons-acons (equal (occ-name-alist-p (hons-acons acl2::a acl2::n acl2::x)) (and (occ-name-p acl2::a) (occ-name-list-p acl2::n) (occ-name-alist-p acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-list-p-of-cdr-of-hons-assoc-equal-when-occ-name-alist-p (implies (occ-name-alist-p acl2::x) (iff (occ-name-list-p (cdr (hons-assoc-equal acl2::k acl2::x))) (or (hons-assoc-equal acl2::k acl2::x) (occ-name-list-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-list-p-of-cdar-when-occ-name-alist-p (implies (occ-name-alist-p acl2::x) (iff (occ-name-list-p (cdar acl2::x)) (or (consp acl2::x) (occ-name-list-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm occ-name-p-of-caar-when-occ-name-alist-p (implies (occ-name-alist-p acl2::x) (iff (occ-name-p (caar acl2::x)) (or (consp acl2::x) (occ-name-p nil)))) :rule-classes ((:rewrite)))