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Logops-bit-functions

B-andc2

And of bitps, complementing the second.

Signature
(b-andc2 i j) → bit
Arguments: i — Guard (bitp i).; j — Guard (bitp j).
Returns: bit — Type (bitp bit).

Definitions and Theorems

Function: b-andc2$inline

(defun b-andc2$inline (i j)
  (declare (xargs :guard (and (bitp i) (bitp j))))
  (let ((__function__ 'b-andc2))
    (declare (ignorable __function__))
    (mbe :logic (if (zbp i) 0 (if (zbp j) 1 0))
         :exec (the (unsigned-byte 1)
                    (logandc2 (the (unsigned-byte 1) i)
                              (the (unsigned-byte 1) j))))))

Theorem: bitp-of-b-andc2

(defthm bitp-of-b-andc2
  (b* ((bit (b-andc2$inline i j)))
    (bitp bit))
  :rule-classes :type-prescription)