Recognizer for atc-symbol-fninfo-alist.
(atc-symbol-fninfo-alistp x) → *
Function:
(defun atc-symbol-fninfo-alistp (x) (declare (xargs :guard t)) (let ((__function__ 'atc-symbol-fninfo-alistp)) (declare (ignorable __function__)) (if (atom x) (eq x nil) (and (consp (car x)) (symbolp (caar x)) (atc-fn-infop (cdar x)) (atc-symbol-fninfo-alistp (cdr x))))))
Theorem:
(defthm atc-symbol-fninfo-alistp-of-append (equal (atc-symbol-fninfo-alistp (append acl2::a acl2::b)) (and (atc-symbol-fninfo-alistp (list-fix acl2::a)) (atc-symbol-fninfo-alistp acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-symbol-fninfo-alistp-of-rev (equal (atc-symbol-fninfo-alistp (rev acl2::x)) (atc-symbol-fninfo-alistp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-symbol-fninfo-alistp-of-list-fix (implies (atc-symbol-fninfo-alistp acl2::x) (atc-symbol-fninfo-alistp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-atc-symbol-fninfo-alistp-compound-recognizer (implies (atc-symbol-fninfo-alistp acl2::x) (true-listp acl2::x)) :rule-classes :compound-recognizer)
Theorem:
(defthm atc-symbol-fninfo-alistp-when-not-consp (implies (not (consp acl2::x)) (equal (atc-symbol-fninfo-alistp acl2::x) (not acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-symbol-fninfo-alistp-of-cdr-when-atc-symbol-fninfo-alistp (implies (atc-symbol-fninfo-alistp (double-rewrite acl2::x)) (atc-symbol-fninfo-alistp (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-symbol-fninfo-alistp-of-cons (equal (atc-symbol-fninfo-alistp (cons acl2::a acl2::x)) (and (and (consp acl2::a) (symbolp (car acl2::a)) (atc-fn-infop (cdr acl2::a))) (atc-symbol-fninfo-alistp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-symbol-fninfo-alistp-of-remove-assoc (implies (atc-symbol-fninfo-alistp acl2::x) (atc-symbol-fninfo-alistp (remove-assoc-equal acl2::name acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-symbol-fninfo-alistp-of-put-assoc (implies (and (atc-symbol-fninfo-alistp acl2::x)) (iff (atc-symbol-fninfo-alistp (put-assoc-equal acl2::name acl2::val acl2::x)) (and (symbolp acl2::name) (atc-fn-infop acl2::val)))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-symbol-fninfo-alistp-of-fast-alist-clean (implies (atc-symbol-fninfo-alistp acl2::x) (atc-symbol-fninfo-alistp (fast-alist-clean acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-symbol-fninfo-alistp-of-hons-shrink-alist (implies (and (atc-symbol-fninfo-alistp acl2::x) (atc-symbol-fninfo-alistp acl2::y)) (atc-symbol-fninfo-alistp (hons-shrink-alist acl2::x acl2::y))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-symbol-fninfo-alistp-of-hons-acons (equal (atc-symbol-fninfo-alistp (hons-acons acl2::a acl2::n acl2::x)) (and (symbolp acl2::a) (atc-fn-infop acl2::n) (atc-symbol-fninfo-alistp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm atc-fn-infop-of-cdr-of-hons-assoc-equal-when-atc-symbol-fninfo-alistp (implies (atc-symbol-fninfo-alistp acl2::x) (iff (atc-fn-infop (cdr (hons-assoc-equal acl2::k acl2::x))) (hons-assoc-equal acl2::k acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm alistp-when-atc-symbol-fninfo-alistp-rewrite (implies (atc-symbol-fninfo-alistp acl2::x) (alistp acl2::x)) :rule-classes ((:rewrite)))
Theorem:
(defthm alistp-when-atc-symbol-fninfo-alistp (implies (atc-symbol-fninfo-alistp acl2::x) (alistp acl2::x)) :rule-classes :tau-system)
Theorem:
(defthm atc-fn-infop-of-cdar-when-atc-symbol-fninfo-alistp (implies (atc-symbol-fninfo-alistp acl2::x) (iff (atc-fn-infop (cdar acl2::x)) (consp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm symbolp-of-caar-when-atc-symbol-fninfo-alistp (implies (atc-symbol-fninfo-alistp acl2::x) (symbolp (caar acl2::x))) :rule-classes ((:rewrite)))