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• Binary

Take-leading-bin-digit-chars

Collect any leading 0-1 characters from the start of a character list.

Signature

(take-leading-bin-digit-chars x) → head

Arguments

x — Guard (character-listp x).

Returns

head — Type (character-listp head).

Definitions and Theorems

Function: take-leading-bin-digit-chars

(defun take-leading-bin-digit-chars (x)
  (declare (xargs :guard (character-listp x)))
  (let ((acl2::__function__ 'take-leading-bin-digit-chars))
    (declare (ignorable acl2::__function__))
    (cond ((atom x) nil)
          ((bin-digit-char-p (car x))
           (cons (car x)
                 (take-leading-bin-digit-chars (cdr x))))
          (t nil))))

Theorem: character-listp-of-take-leading-bin-digit-chars

(defthm character-listp-of-take-leading-bin-digit-chars
  (b* ((head (take-leading-bin-digit-chars x)))
    (character-listp head))
  :rule-classes :rewrite)

Theorem: icharlisteqv-implies-equal-take-leading-bin-digit-chars-1

(defthm icharlisteqv-implies-equal-take-leading-bin-digit-chars-1
  (implies (icharlisteqv x x-equiv)
           (equal (take-leading-bin-digit-chars x)
                  (take-leading-bin-digit-chars x-equiv)))
  :rule-classes (:congruence))

Theorem: bin-digit-char-list*p-of-take-leading-bin-digit-chars

(defthm bin-digit-char-list*p-of-take-leading-bin-digit-chars
  (bin-digit-char-list*p (take-leading-bin-digit-chars x)))

Theorem: bound-of-len-of-take-leading-bin-digit-chars

(defthm bound-of-len-of-take-leading-bin-digit-chars
  (<= (len (take-leading-bin-digit-chars x))
      (len x))
  :rule-classes :linear)

Theorem: equal-of-take-leading-bin-digit-chars-and-length

(defthm equal-of-take-leading-bin-digit-chars-and-length
  (equal (equal (len (take-leading-bin-digit-chars x))
                (len x))
         (bin-digit-char-list*p x)))

Theorem: take-leading-bin-digit-chars-when-bin-digit-char-list*p

(defthm take-leading-bin-digit-chars-when-bin-digit-char-list*p
  (implies (bin-digit-char-list*p x)
           (equal (take-leading-bin-digit-chars x)
                  (list-fix x))))

Theorem: consp-of-take-leading-bin-digit-chars

(defthm consp-of-take-leading-bin-digit-chars
  (equal (consp (take-leading-bin-digit-chars x))
         (bin-digit-char-p (car x))))