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Sparseint

Sparseint-length

Compute the integer-length of a sparseint. Returns an integer, not a sparseint.

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

Definitions and Theorems

Function: sparseint-length$inline

(defun sparseint-length$inline (x)
  (declare (xargs :guard (sparseint-p x)))
  (let ((__function__ 'sparseint-length))
    (declare (ignorable __function__))
    (sparseint$-length (sparseint-fix x))))

Theorem: natp-of-sparseint-length

(defthm natp-of-sparseint-length
  (b* ((length (sparseint-length$inline x)))
    (natp length))
  :rule-classes :type-prescription)

Theorem: sparseint-length-correct

(defthm sparseint-length-correct
  (b* ((common-lisp::?length (sparseint-length$inline x)))
    (equal length
           (integer-length (sparseint-val x)))))

Theorem: sparseint-length$inline-of-sparseint-fix-x

(defthm sparseint-length$inline-of-sparseint-fix-x
  (equal (sparseint-length$inline (sparseint-fix x))
         (sparseint-length$inline x)))

Theorem: sparseint-length$inline-sparseint-equiv-congruence-on-x

(defthm sparseint-length$inline-sparseint-equiv-congruence-on-x
  (implies (sparseint-equiv x x-equiv)
           (equal (sparseint-length$inline x)
                  (sparseint-length$inline x-equiv)))
  :rule-classes :congruence)