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Code-segment-descriptorbits

!code-segment-descriptorbits->r

Update the |ACL2|::|R| field of a code-segment-descriptorbits bit structure.

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

Definitions and Theorems

Function: !code-segment-descriptorbits->r$inline

(defun !code-segment-descriptorbits->r$inline (r x)
 (declare (xargs :guard (and (bitp r)
                             (code-segment-descriptorbits-p x))))
 (mbe
   :logic
   (b* ((r (mbe :logic (bfix r) :exec r))
        (x (code-segment-descriptorbits-fix x)))
     (part-install r 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) r) 41))))))

Theorem: code-segment-descriptorbits-p-of-!code-segment-descriptorbits->r

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

Theorem: !code-segment-descriptorbits->r$inline-of-bfix-r

(defthm !code-segment-descriptorbits->r$inline-of-bfix-r
  (equal (!code-segment-descriptorbits->r$inline (bfix r)
                                                 x)
         (!code-segment-descriptorbits->r$inline r x)))

Theorem: !code-segment-descriptorbits->r$inline-bit-equiv-congruence-on-r

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

Theorem: !code-segment-descriptorbits->r$inline-of-code-segment-descriptorbits-fix-x

(defthm
 !code-segment-descriptorbits->r$inline-of-code-segment-descriptorbits-fix-x
 (equal (!code-segment-descriptorbits->r$inline
             r (code-segment-descriptorbits-fix x))
        (!code-segment-descriptorbits->r$inline r x)))

Theorem: !code-segment-descriptorbits->r$inline-code-segment-descriptorbits-equiv-congruence-on-x

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

Theorem: !code-segment-descriptorbits->r-is-code-segment-descriptorbits

(defthm
     !code-segment-descriptorbits->r-is-code-segment-descriptorbits
  (equal (!code-segment-descriptorbits->r r x)
         (change-code-segment-descriptorbits x
                                             :r r)))

Theorem: code-segment-descriptorbits->r-of-!code-segment-descriptorbits->r

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

Theorem: !code-segment-descriptorbits->r-equiv-under-mask

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