Basic theorems about congruence-rulelist-p, generated by deflist.
Theorem:
(defthm congruence-rulelist-p-of-cons (equal (congruence-rulelist-p (cons a x)) (and (cmr::congruence-rule-p a) (congruence-rulelist-p x))) :rule-classes ((:rewrite)))
Theorem:
(defthm congruence-rulelist-p-of-cdr-when-congruence-rulelist-p (implies (congruence-rulelist-p (double-rewrite x)) (congruence-rulelist-p (cdr x))) :rule-classes ((:rewrite)))
Theorem:
(defthm congruence-rulelist-p-when-not-consp (implies (not (consp x)) (equal (congruence-rulelist-p x) (not x))) :rule-classes ((:rewrite)))
Theorem:
(defthm congruence-rule-p-of-car-when-congruence-rulelist-p (implies (congruence-rulelist-p x) (iff (cmr::congruence-rule-p (car x)) (or (consp x) (cmr::congruence-rule-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-congruence-rulelist-p-compound-recognizer (implies (congruence-rulelist-p x) (true-listp x)) :rule-classes :compound-recognizer)
Theorem:
(defthm congruence-rulelist-p-of-list-fix (implies (congruence-rulelist-p x) (congruence-rulelist-p (list-fix x))) :rule-classes ((:rewrite)))