Basic theorems about integerp-of-svex-extn-list-p, generated by std::deflist.
Theorem:
(defthm integerp-of-svex-extn-list-p-of-cons (equal (integerp-of-svex-extn-list-p (cons acl2::a acl2::x)) (and (integerp-of-svex-extn-p acl2::a) (integerp-of-svex-extn-list-p acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm integerp-of-svex-extn-list-p-of-cdr-when-integerp-of-svex-extn-list-p (implies (integerp-of-svex-extn-list-p (double-rewrite acl2::x)) (integerp-of-svex-extn-list-p (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm integerp-of-svex-extn-list-p-when-not-consp (implies (not (consp acl2::x)) (equal (integerp-of-svex-extn-list-p acl2::x) (not acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm integerp-of-svex-extn-p-of-car-when-integerp-of-svex-extn-list-p (implies (integerp-of-svex-extn-list-p acl2::x) (iff (integerp-of-svex-extn-p (car acl2::x)) (or (consp acl2::x) (integerp-of-svex-extn-p nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-integerp-of-svex-extn-list-p-compound-recognizer (implies (integerp-of-svex-extn-list-p acl2::x) (true-listp acl2::x)) :rule-classes :compound-recognizer)
Theorem:
(defthm integerp-of-svex-extn-list-p-of-list-fix (implies (integerp-of-svex-extn-list-p acl2::x) (integerp-of-svex-extn-list-p (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm integerp-of-svex-extn-list-p-of-rev (equal (integerp-of-svex-extn-list-p (rev acl2::x)) (integerp-of-svex-extn-list-p (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm integerp-of-svex-extn-list-p-of-append (equal (integerp-of-svex-extn-list-p (append acl2::a acl2::b)) (and (integerp-of-svex-extn-list-p (list-fix acl2::a)) (integerp-of-svex-extn-list-p acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm integerp-of-svex-extn-list-p-of-repeat (iff (integerp-of-svex-extn-list-p (repeat acl2::n acl2::x)) (or (integerp-of-svex-extn-p acl2::x) (zp acl2::n))) :rule-classes ((:rewrite)))