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Sparseint

Sparseint-bitandc2

Compute the logandc2 of two sparseints.

Signature
(sparseint-bitandc2 x y) → res
Arguments: x — Guard (sparseint-p x).; y — Guard (sparseint-p y).
Returns: res — Type (sparseint-p res).

Definitions and Theorems

Function: sparseint-bitandc2$inline

(defun sparseint-bitandc2$inline (x y)
  (declare (xargs :guard (and (sparseint-p x) (sparseint-p y))))
  (let ((__function__ 'sparseint-bitandc2))
    (declare (ignorable __function__))
    (sparseint-binary-bitop 2 x y)))

Theorem: sparseint-p-of-sparseint-bitandc2

(defthm sparseint-p-of-sparseint-bitandc2
  (b* ((res (sparseint-bitandc2$inline x y)))
    (sparseint-p res))
  :rule-classes :type-prescription)

Theorem: sparseint-bitandc2-correct

(defthm sparseint-bitandc2-correct
  (b* ((?res (sparseint-bitandc2$inline x y)))
    (equal (sparseint-val res)
           (logandc2 (sparseint-val x)
                     (sparseint-val y)))))

Theorem: sparseint-bitandc2$inline-of-sparseint-fix-x

(defthm sparseint-bitandc2$inline-of-sparseint-fix-x
  (equal (sparseint-bitandc2$inline (sparseint-fix x)
                                    y)
         (sparseint-bitandc2$inline x y)))

Theorem: sparseint-bitandc2$inline-sparseint-equiv-congruence-on-x

(defthm sparseint-bitandc2$inline-sparseint-equiv-congruence-on-x
  (implies (sparseint-equiv x x-equiv)
           (equal (sparseint-bitandc2$inline x y)
                  (sparseint-bitandc2$inline x-equiv y)))
  :rule-classes :congruence)

Theorem: sparseint-bitandc2$inline-of-sparseint-fix-y

(defthm sparseint-bitandc2$inline-of-sparseint-fix-y
  (equal (sparseint-bitandc2$inline x (sparseint-fix y))
         (sparseint-bitandc2$inline x y)))

Theorem: sparseint-bitandc2$inline-sparseint-equiv-congruence-on-y

(defthm sparseint-bitandc2$inline-sparseint-equiv-congruence-on-y
  (implies (sparseint-equiv y y-equiv)
           (equal (sparseint-bitandc2$inline x y)
                  (sparseint-bitandc2$inline x y-equiv)))
  :rule-classes :congruence)