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Data-segment-descriptorbits

!data-segment-descriptorbits->e

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

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

Definitions and Theorems

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

(defun !data-segment-descriptorbits->e$inline (e x)
 (declare (xargs :guard (and (bitp e)
                             (data-segment-descriptorbits-p x))))
 (mbe
   :logic
   (b* ((e (mbe :logic (bfix e) :exec e))
        (x (data-segment-descriptorbits-fix x)))
     (part-install e x :width 1 :low 42))
   :exec
   (the (unsigned-byte 64)
        (logior (the (unsigned-byte 64)
                     (logand (the (unsigned-byte 64) x)
                             (the (signed-byte 44) -4398046511105)))
                (the (unsigned-byte 43)
                     (ash (the (unsigned-byte 1) e) 42))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !data-segment-descriptorbits->e-equiv-under-mask
  (b* ((?new-x (!data-segment-descriptorbits->e$inline e x)))
    (data-segment-descriptorbits-equiv-under-mask
         new-x x -4398046511105)))