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