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Simpcode

Simpcode->xor

Access the |ACL2|::|XOR| field of a simpcode bit structure.

Signature
(simpcode->xor x) → xor
Arguments: x — Guard (simpcode-p x).
Returns: xor — Type (bitp xor).

Definitions and Theorems

Function: simpcode->xor

(defun simpcode->xor (x)
 (declare (xargs :guard (simpcode-p x)))
 (mbe
     :logic
     (let ((x (simpcode-fix x)))
       (part-select x :low 1 :width 1))
     :exec (the (unsigned-byte 1)
                (logand (the (unsigned-byte 1) 1)
                        (the (unsigned-byte 3)
                             (ash (the (unsigned-byte 4) x) -1))))))

Theorem: bitp-of-simpcode->xor

(defthm bitp-of-simpcode->xor
  (b* ((xor (simpcode->xor x)))
    (bitp xor))
  :rule-classes :rewrite)

Theorem: simpcode->xor-of-simpcode-fix-x

(defthm simpcode->xor-of-simpcode-fix-x
  (equal (simpcode->xor (simpcode-fix x))
         (simpcode->xor x)))

Theorem: simpcode->xor-simpcode-equiv-congruence-on-x

(defthm simpcode->xor-simpcode-equiv-congruence-on-x
  (implies (simpcode-equiv x x-equiv)
           (equal (simpcode->xor x)
                  (simpcode->xor x-equiv)))
  :rule-classes :congruence)

Theorem: simpcode->xor-of-simpcode

(defthm simpcode->xor-of-simpcode
  (equal (simpcode->xor (simpcode neg xor identity choice))
         (bfix xor)))

Theorem: simpcode->xor-of-write-with-mask

(defthm simpcode->xor-of-write-with-mask
 (implies
  (and
   (fty::bitstruct-read-over-write-hyps x simpcode-equiv-under-mask)
   (simpcode-equiv-under-mask x acl2::y fty::mask)
   (equal (logand (lognot fty::mask) 2) 0))
  (equal (simpcode->xor x)
         (simpcode->xor acl2::y))))