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Sparseint

Sparseint-rightshift

Right-shift a sparseint by some shift amount

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

Definitions and Theorems

Function: sparseint-rightshift$inline

(defun sparseint-rightshift$inline (shift x)
  (declare (xargs :guard (and (natp shift) (sparseint-p x))))
  (let ((__function__ 'sparseint-rightshift))
    (declare (ignorable __function__))
    (sparseint$-rightshift shift (sparseint-fix x))))

Theorem: sparseint-p-of-sparseint-rightshift

(defthm sparseint-p-of-sparseint-rightshift
  (b* ((rightshift (sparseint-rightshift$inline shift x)))
    (sparseint-p rightshift))
  :rule-classes :rewrite)

Theorem: sparseint-rightshift-correct

(defthm sparseint-rightshift-correct
  (b* ((?rightshift (sparseint-rightshift$inline shift x)))
    (equal (sparseint-val rightshift)
           (logtail shift (sparseint-val x)))))

Theorem: sparseint-rightshift$inline-of-nfix-shift

(defthm sparseint-rightshift$inline-of-nfix-shift
  (equal (sparseint-rightshift$inline (nfix shift)
                                      x)
         (sparseint-rightshift$inline shift x)))

Theorem: sparseint-rightshift$inline-nat-equiv-congruence-on-shift

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

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

(defthm sparseint-rightshift$inline-of-sparseint-fix-x
  (equal (sparseint-rightshift$inline shift (sparseint-fix x))
         (sparseint-rightshift$inline shift x)))

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

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