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System-segment-descriptorbits

System-segment-descriptorbits->res2

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

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

Definitions and Theorems

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

(defun system-segment-descriptorbits->res2$inline (x)
  (declare (xargs :guard (system-segment-descriptorbits-p x)))
  (mbe :logic
       (let ((x (system-segment-descriptorbits-fix x)))
         (part-select x :low 96 :width 8))
       :exec (the (unsigned-byte 8)
                  (logand (the (unsigned-byte 8) 255)
                          (the (unsigned-byte 32)
                               (ash (the (unsigned-byte 128) x)
                                    -96))))))

Theorem: 8bits-p-of-system-segment-descriptorbits->res2

(defthm 8bits-p-of-system-segment-descriptorbits->res2
  (b* ((res2 (system-segment-descriptorbits->res2$inline x)))
    (8bits-p res2))
  :rule-classes :rewrite)

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
             (system-segment-descriptorbits-fix x))
        (system-segment-descriptorbits->res2$inline 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 x)
             (system-segment-descriptorbits->res2$inline x-equiv)))
 :rule-classes :congruence)

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

(defthm
 system-segment-descriptorbits->res2-of-system-segment-descriptorbits
 (equal (system-segment-descriptorbits->res2
             (system-segment-descriptorbits
                  limit15-0 base15-0 base23-16 type
                  s dpl p limit19-16 avl res1 g base31-24
                  base63-32 res2 all-zeroes? res3))
        (8bits-fix res2)))

Theorem: system-segment-descriptorbits->res2-of-write-with-mask

(defthm system-segment-descriptorbits->res2-of-write-with-mask
 (implies
  (and
      (fty::bitstruct-read-over-write-hyps
           x
           system-segment-descriptorbits-equiv-under-mask)
      (system-segment-descriptorbits-equiv-under-mask x y fty::mask)
      (equal (logand (lognot fty::mask)
                     20203181441137406086353707335680)
             0))
  (equal (system-segment-descriptorbits->res2 x)
         (system-segment-descriptorbits->res2 y))))