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Sparseint

Sparseint-bitnot

Bitwise negation of a sparseint

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

Definitions and Theorems

Function: sparseint-bitnot$inline

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

Theorem: sparseint-p-of-sparseint-bitnot

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

Theorem: sparseint-val-of-sparseint-bitnot

(defthm sparseint-val-of-sparseint-bitnot
  (b* ((?bitnot (sparseint-bitnot$inline x)))
    (equal (sparseint-val bitnot)
           (lognot (sparseint-val x)))))

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

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

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

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