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System-segment-descriptorbits

!system-segment-descriptorbits->g

Update the |X86ISA|::|G| field of a system-segment-descriptorbits bit structure.

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

Definitions and Theorems

Function: !system-segment-descriptorbits->g$inline

(defun !system-segment-descriptorbits->g$inline (g x)
 (declare (xargs :guard (and (bitp g)
                             (system-segment-descriptorbits-p x))))
 (mbe
     :logic
     (b* ((g (mbe :logic (bfix g) :exec g))
          (x (system-segment-descriptorbits-fix x)))
       (part-install g x :width 1 :low 55))
     :exec (the (unsigned-byte 128)
                (logior (the (unsigned-byte 128)
                             (logand (the (unsigned-byte 128) x)
                                     (the (signed-byte 57)
                                          -36028797018963969)))
                        (the (unsigned-byte 56)
                             (ash (the (unsigned-byte 1) g) 55))))))

Theorem: system-segment-descriptorbits-p-of-!system-segment-descriptorbits->g

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

Theorem: !system-segment-descriptorbits->g$inline-of-bfix-g

(defthm !system-segment-descriptorbits->g$inline-of-bfix-g
  (equal (!system-segment-descriptorbits->g$inline (bfix g)
                                                   x)
         (!system-segment-descriptorbits->g$inline g x)))

Theorem: !system-segment-descriptorbits->g$inline-bit-equiv-congruence-on-g

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

Theorem: !system-segment-descriptorbits->g$inline-of-system-segment-descriptorbits-fix-x

(defthm
 !system-segment-descriptorbits->g$inline-of-system-segment-descriptorbits-fix-x
 (equal (!system-segment-descriptorbits->g$inline
             g (system-segment-descriptorbits-fix x))
        (!system-segment-descriptorbits->g$inline g x)))

Theorem: !system-segment-descriptorbits->g$inline-system-segment-descriptorbits-equiv-congruence-on-x

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

Theorem: !system-segment-descriptorbits->g-is-system-segment-descriptorbits

(defthm
 !system-segment-descriptorbits->g-is-system-segment-descriptorbits
 (equal (!system-segment-descriptorbits->g g x)
        (change-system-segment-descriptorbits x
                                              :g g)))

Theorem: system-segment-descriptorbits->g-of-!system-segment-descriptorbits->g

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

Theorem: !system-segment-descriptorbits->g-equiv-under-mask

(defthm !system-segment-descriptorbits->g-equiv-under-mask
  (b* ((?new-x (!system-segment-descriptorbits->g$inline g x)))
    (system-segment-descriptorbits-equiv-under-mask
         new-x x -36028797018963969)))