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Code-segment-descriptorbits

!code-segment-descriptorbits->d

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

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

Definitions and Theorems

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

(defun !code-segment-descriptorbits->d$inline (d x)
 (declare (xargs :guard (and (bitp d)
                             (code-segment-descriptorbits-p x))))
 (mbe
     :logic
     (b* ((d (mbe :logic (bfix d) :exec d))
          (x (code-segment-descriptorbits-fix x)))
       (part-install d x :width 1 :low 54))
     :exec (the (unsigned-byte 64)
                (logior (the (unsigned-byte 64)
                             (logand (the (unsigned-byte 64) x)
                                     (the (signed-byte 56)
                                          -18014398509481985)))
                        (the (unsigned-byte 55)
                             (ash (the (unsigned-byte 1) d) 54))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !code-segment-descriptorbits->d-equiv-under-mask
  (b* ((?new-x (!code-segment-descriptorbits->d$inline d x)))
    (code-segment-descriptorbits-equiv-under-mask
         new-x x -18014398509481985)))