Basic theorems about alternative-spec-listp, generated by std::deflist.
Theorem:
(defthm alternative-spec-listp-of-cons (equal (alternative-spec-listp (cons acl2::a acl2::x)) (and (alternative-specp acl2::a) (alternative-spec-listp acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-spec-listp-of-cdr-when-alternative-spec-listp (implies (alternative-spec-listp (double-rewrite acl2::x)) (alternative-spec-listp (cdr acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-spec-listp-when-not-consp (implies (not (consp acl2::x)) (equal (alternative-spec-listp acl2::x) (not acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-specp-of-car-when-alternative-spec-listp (implies (alternative-spec-listp acl2::x) (iff (alternative-specp (car acl2::x)) (or (consp acl2::x) (alternative-specp nil)))) :rule-classes ((:rewrite)))
Theorem:
(defthm true-listp-when-alternative-spec-listp-compound-recognizer (implies (alternative-spec-listp acl2::x) (true-listp acl2::x)) :rule-classes :compound-recognizer)
Theorem:
(defthm alternative-spec-listp-of-list-fix (implies (alternative-spec-listp acl2::x) (alternative-spec-listp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-spec-listp-of-rev (equal (alternative-spec-listp (rev acl2::x)) (alternative-spec-listp (list-fix acl2::x))) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-spec-listp-of-append (equal (alternative-spec-listp (append acl2::a acl2::b)) (and (alternative-spec-listp (list-fix acl2::a)) (alternative-spec-listp acl2::b))) :rule-classes ((:rewrite)))
Theorem:
(defthm alternative-specp-of-nth-when-alternative-spec-listp (implies (and (alternative-spec-listp acl2::x) (< (nfix acl2::n) (len acl2::x))) (alternative-specp (nth acl2::n acl2::x))) :rule-classes ((:rewrite)))