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Data-segment-descriptorbits

!data-segment-descriptorbits->p

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

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

Definitions and Theorems

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

(defun !data-segment-descriptorbits->p$inline (p x)
 (declare (xargs :guard (and (bitp p)
                             (data-segment-descriptorbits-p x))))
 (mbe
     :logic
     (b* ((p (mbe :logic (bfix p) :exec p))
          (x (data-segment-descriptorbits-fix x)))
       (part-install p x :width 1 :low 47))
     :exec (the (unsigned-byte 64)
                (logior (the (unsigned-byte 64)
                             (logand (the (unsigned-byte 64) x)
                                     (the (signed-byte 49)
                                          -140737488355329)))
                        (the (unsigned-byte 48)
                             (ash (the (unsigned-byte 1) p) 47))))))

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

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

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

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

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

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

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
             p (data-segment-descriptorbits-fix x))
        (!data-segment-descriptorbits->p$inline p 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 p x)
             (!data-segment-descriptorbits->p$inline p x-equiv)))
 :rule-classes :congruence)

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

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

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

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

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

(defthm !data-segment-descriptorbits->p-equiv-under-mask
  (b* ((?new-x (!data-segment-descriptorbits->p$inline p x)))
    (data-segment-descriptorbits-equiv-under-mask
         new-x x -140737488355329)))