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Data-segment-descriptorbits

Data-segment-descriptorbits->p

Access the |ACL2|::|P| field of a data-segment-descriptorbits bit structure.

Signature
(data-segment-descriptorbits->p x) → p
Arguments: x — Guard (data-segment-descriptorbits-p x).
Returns: p — Type (bitp p).

Definitions and Theorems

Function: data-segment-descriptorbits->p$inline

(defun data-segment-descriptorbits->p$inline (x)
  (declare (xargs :guard (data-segment-descriptorbits-p x)))
  (mbe :logic
       (let ((x (data-segment-descriptorbits-fix x)))
         (part-select x :low 47 :width 1))
       :exec (the (unsigned-byte 1)
                  (logand (the (unsigned-byte 1) 1)
                          (the (unsigned-byte 17)
                               (ash (the (unsigned-byte 64) x)
                                    -47))))))

Theorem: bitp-of-data-segment-descriptorbits->p

(defthm bitp-of-data-segment-descriptorbits->p
  (b* ((p (data-segment-descriptorbits->p$inline x)))
    (bitp p))
  :rule-classes :rewrite)

Theorem: data-segment-descriptorbits->p$inline-of-data-segment-descriptorbits-fix-x

(defthm
 data-segment-descriptorbits->p$inline-of-data-segment-descriptorbits-fix-x
 (equal (data-segment-descriptorbits->p$inline
             (data-segment-descriptorbits-fix x))
        (data-segment-descriptorbits->p$inline x)))

Theorem: data-segment-descriptorbits->p$inline-data-segment-descriptorbits-equiv-congruence-on-x

(defthm
 data-segment-descriptorbits->p$inline-data-segment-descriptorbits-equiv-congruence-on-x
 (implies (data-segment-descriptorbits-equiv x x-equiv)
          (equal (data-segment-descriptorbits->p$inline x)
                 (data-segment-descriptorbits->p$inline x-equiv)))
 :rule-classes :congruence)

Theorem: data-segment-descriptorbits->p-of-data-segment-descriptorbits

(defthm
      data-segment-descriptorbits->p-of-data-segment-descriptorbits
  (equal (data-segment-descriptorbits->p
              (data-segment-descriptorbits
                   limit15-0
                   base15-0 base23-16 a w e msb-of-type s
                   dpl p limit19-16 avl l d/b g base31-24))
         (bfix p)))

Theorem: data-segment-descriptorbits->p-of-write-with-mask

(defthm data-segment-descriptorbits->p-of-write-with-mask
 (implies
   (and (fty::bitstruct-read-over-write-hyps
             x
             data-segment-descriptorbits-equiv-under-mask)
        (data-segment-descriptorbits-equiv-under-mask x y fty::mask)
        (equal (logand (lognot fty::mask)
                       140737488355328)
               0))
   (equal (data-segment-descriptorbits->p x)
          (data-segment-descriptorbits->p y))))