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