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Code-segment-descriptorbits

!code-segment-descriptorbits->dpl

Update the |X86ISA|::|DPL| field of a code-segment-descriptorbits bit structure.

Signature
(!code-segment-descriptorbits->dpl dpl x) → new-x
Arguments: dpl — Guard (2bits-p dpl).; x — Guard (code-segment-descriptorbits-p x).
Returns: new-x — Type (code-segment-descriptorbits-p new-x).

Definitions and Theorems

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

(defun !code-segment-descriptorbits->dpl$inline (dpl x)
  (declare (xargs :guard (and (2bits-p dpl)
                              (code-segment-descriptorbits-p x))))
  (mbe :logic
       (b* ((dpl (mbe :logic (2bits-fix dpl) :exec dpl))
            (x (code-segment-descriptorbits-fix x)))
         (part-install dpl x :width 2 :low 45))
       :exec (the (unsigned-byte 64)
                  (logior (the (unsigned-byte 64)
                               (logand (the (unsigned-byte 64) x)
                                       (the (signed-byte 48)
                                            -105553116266497)))
                          (the (unsigned-byte 47)
                               (ash (the (unsigned-byte 2) dpl)
                                    45))))))

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

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

Theorem: !code-segment-descriptorbits->dpl$inline-of-2bits-fix-dpl

(defthm !code-segment-descriptorbits->dpl$inline-of-2bits-fix-dpl
  (equal (!code-segment-descriptorbits->dpl$inline (2bits-fix dpl)
                                                   x)
         (!code-segment-descriptorbits->dpl$inline dpl x)))

Theorem: !code-segment-descriptorbits->dpl$inline-2bits-equiv-congruence-on-dpl

(defthm
 !code-segment-descriptorbits->dpl$inline-2bits-equiv-congruence-on-dpl
 (implies
     (2bits-equiv dpl dpl-equiv)
     (equal (!code-segment-descriptorbits->dpl$inline dpl x)
            (!code-segment-descriptorbits->dpl$inline dpl-equiv x)))
 :rule-classes :congruence)

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

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

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

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

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

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

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

(defthm
 code-segment-descriptorbits->dpl-of-!code-segment-descriptorbits->dpl
 (b* ((?new-x (!code-segment-descriptorbits->dpl$inline dpl x)))
   (equal (code-segment-descriptorbits->dpl new-x)
          (2bits-fix dpl))))

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

(defthm !code-segment-descriptorbits->dpl-equiv-under-mask
  (b* ((?new-x (!code-segment-descriptorbits->dpl$inline dpl x)))
    (code-segment-descriptorbits-equiv-under-mask
         new-x x -105553116266497)))