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Sparseint

Sparseint-trailing-1-count

Count the trailing consecutive 1s of a sparseint.

Signature
(sparseint-trailing-1-count x) → count
Arguments: x — Guard (sparseint-p x).
Returns: count — Type (natp count).

Definitions and Theorems

Function: sparseint-trailing-1-count

(defun sparseint-trailing-1-count (x)
 (declare (xargs :guard (sparseint-p x)))
 (let ((__function__ 'sparseint-trailing-1-count))
  (declare (ignorable __function__))
  (b*
   ((count (sparseint$-trailing-0-count-rec 0 1 (sparseint-fix x))))
   (or count 0))))

Theorem: natp-of-sparseint-trailing-1-count

(defthm natp-of-sparseint-trailing-1-count
  (b* ((count (sparseint-trailing-1-count x)))
    (natp count))
  :rule-classes :type-prescription)

Theorem: sparseint-trailing-1-count-correct

(defthm sparseint-trailing-1-count-correct
  (b* ((common-lisp::?count (sparseint-trailing-1-count x)))
    (equal count
           (trailing-1-count (sparseint-val x)))))

Theorem: sparseint-trailing-1-count-of-sparseint-fix-x

(defthm sparseint-trailing-1-count-of-sparseint-fix-x
  (equal (sparseint-trailing-1-count (sparseint-fix x))
         (sparseint-trailing-1-count x)))

Theorem: sparseint-trailing-1-count-sparseint-equiv-congruence-on-x

(defthm sparseint-trailing-1-count-sparseint-equiv-congruence-on-x
  (implies (sparseint-equiv x x-equiv)
           (equal (sparseint-trailing-1-count x)
                  (sparseint-trailing-1-count x-equiv)))
  :rule-classes :congruence)