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Data-segment-descriptorbits

!data-segment-descriptorbits->s

Update the |X86ISA|::|S| field of a data-segment-descriptorbits bit structure.

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

Definitions and Theorems

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

(defun !data-segment-descriptorbits->s$inline (s x)
 (declare (xargs :guard (and (bitp s)
                             (data-segment-descriptorbits-p x))))
 (mbe
  :logic
  (b* ((s (mbe :logic (bfix s) :exec s))
       (x (data-segment-descriptorbits-fix x)))
    (part-install s x :width 1 :low 44))
  :exec
  (the (unsigned-byte 64)
       (logior (the (unsigned-byte 64)
                    (logand (the (unsigned-byte 64) x)
                            (the (signed-byte 46) -17592186044417)))
               (the (unsigned-byte 45)
                    (ash (the (unsigned-byte 1) s) 44))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !data-segment-descriptorbits->s-equiv-under-mask
  (b* ((?new-x (!data-segment-descriptorbits->s$inline s x)))
    (data-segment-descriptorbits-equiv-under-mask
         new-x x -17592186044417)))