		Search-engine friendly clone of the ACL2 documentation.

Sparseint

Sparseint-test-bitandc2

Check whether the logandc2 of two sparseints produces a nonzero value.

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

Definitions and Theorems

Function: sparseint-test-bitandc2$inline

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

Theorem: booleanp-of-sparseint-test-bitandc2

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

Theorem: sparseint-test-bitandc2-correct

(defthm sparseint-test-bitandc2-correct
  (b* ((?test (sparseint-test-bitandc2$inline x y)))
    (equal test
           (not (equal 0
                       (logandc2 (sparseint-val x)
                                 (sparseint-val y)))))))

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

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

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

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

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

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

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

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