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• Binary

Nat-to-bin-string-list

Convert a list of natural numbers into a list of bit strings.

Signature

(nat-to-bin-string-list x) → strs

Arguments

x — Guard (nat-listp x).

Returns

strs — Type (string-listp strs).

Definitions and Theorems

Function: nat-to-bin-string-list

(defun nat-to-bin-string-list (x)
  (declare (xargs :guard (nat-listp x)))
  (let ((acl2::__function__ 'nat-to-bin-string-list))
    (declare (ignorable acl2::__function__))
    (if (atom x)
        nil
      (cons (nat-to-bin-string (car x))
            (nat-to-bin-string-list (cdr x))))))

Theorem: string-listp-of-nat-to-bin-string-list

(defthm string-listp-of-nat-to-bin-string-list
  (b* ((strs (nat-to-bin-string-list x)))
    (string-listp strs))
  :rule-classes :rewrite)

Theorem: nat-to-bin-string-list-when-atom

(defthm nat-to-bin-string-list-when-atom
  (implies (atom x)
           (equal (nat-to-bin-string-list x) nil)))

Theorem: nat-to-bin-string-list-of-cons

(defthm nat-to-bin-string-list-of-cons
  (equal (nat-to-bin-string-list (cons a x))
         (cons (nat-to-bin-string a)
               (nat-to-bin-string-list x))))