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Toplevel-listp

Toplevel-listp-basics

Basic theorems about toplevel-listp, generated by std::deflist.

Definitions and Theorems

Theorem: toplevel-listp-of-cons

(defthm toplevel-listp-of-cons
  (equal (toplevel-listp (cons acl2::a acl2::x))
         (and (toplevelp acl2::a)
              (toplevel-listp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: toplevel-listp-of-cdr-when-toplevel-listp

(defthm toplevel-listp-of-cdr-when-toplevel-listp
  (implies (toplevel-listp (double-rewrite acl2::x))
           (toplevel-listp (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: toplevel-listp-when-not-consp

(defthm toplevel-listp-when-not-consp
  (implies (not (consp acl2::x))
           (equal (toplevel-listp acl2::x)
                  (not acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: toplevelp-of-car-when-toplevel-listp

(defthm toplevelp-of-car-when-toplevel-listp
  (implies (toplevel-listp acl2::x)
           (iff (toplevelp (car acl2::x))
                (consp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-toplevel-listp-compound-recognizer

(defthm true-listp-when-toplevel-listp-compound-recognizer
  (implies (toplevel-listp acl2::x)
           (true-listp acl2::x))
  :rule-classes :compound-recognizer)

Theorem: toplevel-listp-of-list-fix

(defthm toplevel-listp-of-list-fix
  (implies (toplevel-listp acl2::x)
           (toplevel-listp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: toplevel-listp-of-rev

(defthm toplevel-listp-of-rev
  (equal (toplevel-listp (rev acl2::x))
         (toplevel-listp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: toplevel-listp-of-append

(defthm toplevel-listp-of-append
  (equal (toplevel-listp (append acl2::a acl2::b))
         (and (toplevel-listp (list-fix acl2::a))
              (toplevel-listp acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: toplevelp-of-nth-when-toplevel-listp

(defthm toplevelp-of-nth-when-toplevel-listp
  (implies (toplevel-listp acl2::x)
           (iff (toplevelp (nth acl2::n acl2::x))
                (< (nfix acl2::n) (len acl2::x))))
  :rule-classes ((:rewrite)))