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System-segment-descriptorbits

!system-segment-descriptorbits->res2

Update the |X86ISA|::|RES2| field of a system-segment-descriptorbits bit structure.

Signature
(!system-segment-descriptorbits->res2 res2 x) → new-x
Arguments: res2 — Guard (8bits-p res2).; x — Guard (system-segment-descriptorbits-p x).
Returns: new-x — Type (system-segment-descriptorbits-p new-x).

Definitions and Theorems

Function: !system-segment-descriptorbits->res2$inline

(defun !system-segment-descriptorbits->res2$inline (res2 x)
 (declare (xargs :guard (and (8bits-p res2)
                             (system-segment-descriptorbits-p x))))
 (mbe
  :logic
  (b* ((res2 (mbe :logic (8bits-fix res2)
                  :exec res2))
       (x (system-segment-descriptorbits-fix x)))
    (part-install res2 x :width 8 :low 96))
  :exec
  (the
      (unsigned-byte 128)
      (logior (the (unsigned-byte 128)
                   (logand (the (unsigned-byte 128) x)
                           (the (signed-byte 105)
                                -20203181441137406086353707335681)))
              (the (unsigned-byte 104)
                   (ash (the (unsigned-byte 8) res2)
                        96))))))

Theorem: system-segment-descriptorbits-p-of-!system-segment-descriptorbits->res2

(defthm
 system-segment-descriptorbits-p-of-!system-segment-descriptorbits->res2
 (b* ((new-x (!system-segment-descriptorbits->res2$inline res2 x)))
   (system-segment-descriptorbits-p new-x))
 :rule-classes :rewrite)

Theorem: !system-segment-descriptorbits->res2$inline-of-8bits-fix-res2

(defthm
      !system-segment-descriptorbits->res2$inline-of-8bits-fix-res2
  (equal
       (!system-segment-descriptorbits->res2$inline (8bits-fix res2)
                                                    x)
       (!system-segment-descriptorbits->res2$inline res2 x)))

Theorem: !system-segment-descriptorbits->res2$inline-8bits-equiv-congruence-on-res2

(defthm
 !system-segment-descriptorbits->res2$inline-8bits-equiv-congruence-on-res2
 (implies
   (8bits-equiv res2 res2-equiv)
   (equal
        (!system-segment-descriptorbits->res2$inline res2 x)
        (!system-segment-descriptorbits->res2$inline res2-equiv x)))
 :rule-classes :congruence)

Theorem: !system-segment-descriptorbits->res2$inline-of-system-segment-descriptorbits-fix-x

(defthm
 !system-segment-descriptorbits->res2$inline-of-system-segment-descriptorbits-fix-x
 (equal (!system-segment-descriptorbits->res2$inline
             res2
             (system-segment-descriptorbits-fix x))
        (!system-segment-descriptorbits->res2$inline res2 x)))

Theorem: !system-segment-descriptorbits->res2$inline-system-segment-descriptorbits-equiv-congruence-on-x

(defthm
 !system-segment-descriptorbits->res2$inline-system-segment-descriptorbits-equiv-congruence-on-x
 (implies
   (system-segment-descriptorbits-equiv x x-equiv)
   (equal
        (!system-segment-descriptorbits->res2$inline res2 x)
        (!system-segment-descriptorbits->res2$inline res2 x-equiv)))
 :rule-classes :congruence)

Theorem: !system-segment-descriptorbits->res2-is-system-segment-descriptorbits

(defthm
 !system-segment-descriptorbits->res2-is-system-segment-descriptorbits
 (equal (!system-segment-descriptorbits->res2 res2 x)
        (change-system-segment-descriptorbits x
                                              :res2 res2)))

Theorem: system-segment-descriptorbits->res2-of-!system-segment-descriptorbits->res2

(defthm
 system-segment-descriptorbits->res2-of-!system-segment-descriptorbits->res2
 (b* ((?new-x (!system-segment-descriptorbits->res2$inline res2 x)))
   (equal (system-segment-descriptorbits->res2 new-x)
          (8bits-fix res2))))

Theorem: !system-segment-descriptorbits->res2-equiv-under-mask

(defthm !system-segment-descriptorbits->res2-equiv-under-mask
 (b* ((?new-x (!system-segment-descriptorbits->res2$inline res2 x)))
   (system-segment-descriptorbits-equiv-under-mask
        new-x
        x -20203181441137406086353707335681)))