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• Binary

Skip-leading-bit-digits

Skip over any leading 0-1 characters at the start of a character list.

Signature

(skip-leading-bit-digits x) → tail

Arguments

x — Guard (character-listp x).

Returns

tail — Type (character-listp tail), given the guard.

Definitions and Theorems

Function: skip-leading-bit-digits

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

Theorem: character-listp-of-skip-leading-bit-digits

(defthm character-listp-of-skip-leading-bit-digits
  (implies (and (character-listp x))
           (b* ((tail (skip-leading-bit-digits x)))
             (character-listp tail)))
  :rule-classes :rewrite)

Theorem: charlisteqv-implies-charlisteqv-skip-leading-bit-digits-1

(defthm charlisteqv-implies-charlisteqv-skip-leading-bit-digits-1
  (implies (charlisteqv x x-equiv)
           (charlisteqv (skip-leading-bit-digits x)
                        (skip-leading-bit-digits x-equiv)))
  :rule-classes (:congruence))

Theorem: icharlisteqv-implies-icharlisteqv-skip-leading-bit-digits-1

(defthm icharlisteqv-implies-icharlisteqv-skip-leading-bit-digits-1
  (implies (icharlisteqv x x-equiv)
           (icharlisteqv (skip-leading-bit-digits x)
                         (skip-leading-bit-digits x-equiv)))
  :rule-classes (:congruence))

Theorem: len-of-skip-leading-bit-digits

(defthm len-of-skip-leading-bit-digits
  (implies (bin-digit-char-p (car x))
           (< (len (skip-leading-bit-digits x))
              (len x))))