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Data-segment-descriptorbits

!data-segment-descriptorbits->w

Update the |ACL2|::|W| field of a data-segment-descriptorbits bit structure.

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

Definitions and Theorems

Function: !data-segment-descriptorbits->w$inline

(defun !data-segment-descriptorbits->w$inline (w x)
 (declare (xargs :guard (and (bitp w)
                             (data-segment-descriptorbits-p x))))
 (mbe
   :logic
   (b* ((w (mbe :logic (bfix w) :exec w))
        (x (data-segment-descriptorbits-fix x)))
     (part-install w x :width 1 :low 41))
   :exec
   (the (unsigned-byte 64)
        (logior (the (unsigned-byte 64)
                     (logand (the (unsigned-byte 64) x)
                             (the (signed-byte 43) -2199023255553)))
                (the (unsigned-byte 42)
                     (ash (the (unsigned-byte 1) w) 41))))))

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

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

Theorem: !data-segment-descriptorbits->w$inline-of-bfix-w

(defthm !data-segment-descriptorbits->w$inline-of-bfix-w
  (equal (!data-segment-descriptorbits->w$inline (bfix w)
                                                 x)
         (!data-segment-descriptorbits->w$inline w x)))

Theorem: !data-segment-descriptorbits->w$inline-bit-equiv-congruence-on-w

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

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

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

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

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

Theorem: !data-segment-descriptorbits->w-is-data-segment-descriptorbits

(defthm
     !data-segment-descriptorbits->w-is-data-segment-descriptorbits
  (equal (!data-segment-descriptorbits->w w x)
         (change-data-segment-descriptorbits x
                                             :w w)))

Theorem: data-segment-descriptorbits->w-of-!data-segment-descriptorbits->w

(defthm
  data-segment-descriptorbits->w-of-!data-segment-descriptorbits->w
  (b* ((?new-x (!data-segment-descriptorbits->w$inline w x)))
    (equal (data-segment-descriptorbits->w new-x)
           (bfix w))))

Theorem: !data-segment-descriptorbits->w-equiv-under-mask

(defthm !data-segment-descriptorbits->w-equiv-under-mask
  (b* ((?new-x (!data-segment-descriptorbits->w$inline w x)))
    (data-segment-descriptorbits-equiv-under-mask
         new-x x -2199023255553)))