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Sparseint

Sparseint-trailing-1-count-from

Count the consecutive 1s of a sparseint starting at the given offset.

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

Definitions and Theorems

Function: sparseint-trailing-1-count-from

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

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

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

Theorem: sparseint-trailing-1-count-from-correct

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

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

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

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

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

Theorem: sparseint-trailing-1-count-from-of-nfix-offset

(defthm sparseint-trailing-1-count-from-of-nfix-offset
  (equal (sparseint-trailing-1-count-from x (nfix offset))
         (sparseint-trailing-1-count-from x offset)))

Theorem: sparseint-trailing-1-count-from-nat-equiv-congruence-on-offset

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