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System-segment-descriptorbits

System-segment-descriptorbits->avl

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

Signature
(system-segment-descriptorbits->avl x) → avl
Arguments: x — Guard (system-segment-descriptorbits-p x).
Returns: avl — Type (bitp avl).

Definitions and Theorems

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

(defun system-segment-descriptorbits->avl$inline (x)
  (declare (xargs :guard (system-segment-descriptorbits-p x)))
  (mbe :logic
       (let ((x (system-segment-descriptorbits-fix x)))
         (part-select x :low 52 :width 1))
       :exec (the (unsigned-byte 1)
                  (logand (the (unsigned-byte 1) 1)
                          (the (unsigned-byte 76)
                               (ash (the (unsigned-byte 128) x)
                                    -52))))))

Theorem: bitp-of-system-segment-descriptorbits->avl

(defthm bitp-of-system-segment-descriptorbits->avl
  (b* ((avl (system-segment-descriptorbits->avl$inline x)))
    (bitp avl))
  :rule-classes :rewrite)

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

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

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

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

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

(defthm
 system-segment-descriptorbits->avl-of-system-segment-descriptorbits
 (equal (system-segment-descriptorbits->avl
             (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))
        (bfix avl)))

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

(defthm system-segment-descriptorbits->avl-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)
                     4503599627370496)
             0))
  (equal (system-segment-descriptorbits->avl x)
         (system-segment-descriptorbits->avl y))))