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Data-segment-descriptorbits

!data-segment-descriptorbits->a

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

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

Definitions and Theorems

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

(defun !data-segment-descriptorbits->a$inline (a x)
 (declare (xargs :guard (and (bitp a)
                             (data-segment-descriptorbits-p x))))
 (mbe
   :logic
   (b* ((a (mbe :logic (bfix a) :exec a))
        (x (data-segment-descriptorbits-fix x)))
     (part-install a x :width 1 :low 40))
   :exec
   (the (unsigned-byte 64)
        (logior (the (unsigned-byte 64)
                     (logand (the (unsigned-byte 64) x)
                             (the (signed-byte 42) -1099511627777)))
                (the (unsigned-byte 41)
                     (ash (the (unsigned-byte 1) a) 40))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !data-segment-descriptorbits->a-equiv-under-mask
  (b* ((?new-x (!data-segment-descriptorbits->a$inline a x)))
    (data-segment-descriptorbits-equiv-under-mask
         new-x x -1099511627777)))