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