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• Binary

Nat-to-bin-string-size

Number of characters in the binary representation of a natural.

Signature

(nat-to-bin-string-size x) → size

Arguments

x — Guard (natp x).

Returns

size — Type (posp size).

Definitions and Theorems

Function: nat-to-bin-string-size$inline

(defun nat-to-bin-string-size$inline (x)
  (declare (xargs :guard (natp x)))
  (let ((acl2::__function__ 'nat-to-bin-string-size))
    (declare (ignorable acl2::__function__))
    (if (zp x) 1 (integer-length x))))

Theorem: posp-of-nat-to-bin-string-size

(defthm posp-of-nat-to-bin-string-size
  (b* ((size (nat-to-bin-string-size$inline x)))
    (posp size))
  :rule-classes :type-prescription)

Theorem: len-of-nat-to-bin-chars

(defthm len-of-nat-to-bin-chars
  (equal (len (nat-to-bin-chars x))
         (nat-to-bin-string-size x)))

Theorem: length-of-nat-to-bin-string

(defthm length-of-nat-to-bin-string
  (equal (length (nat-to-bin-string x))
         (nat-to-bin-string-size x)))