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System-segment-descriptorbits

!system-segment-descriptorbits->avl

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

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

Definitions and Theorems

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

(defun !system-segment-descriptorbits->avl$inline (avl x)
  (declare (xargs :guard (and (bitp avl)
                              (system-segment-descriptorbits-p x))))
  (mbe :logic
       (b* ((avl (mbe :logic (bfix avl) :exec avl))
            (x (system-segment-descriptorbits-fix x)))
         (part-install avl x :width 1 :low 52))
       :exec (the (unsigned-byte 128)
                  (logior (the (unsigned-byte 128)
                               (logand (the (unsigned-byte 128) x)
                                       (the (signed-byte 54)
                                            -4503599627370497)))
                          (the (unsigned-byte 53)
                               (ash (the (unsigned-byte 1) avl)
                                    52))))))

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !system-segment-descriptorbits->avl-equiv-under-mask
  (b* ((?new-x (!system-segment-descriptorbits->avl$inline avl x)))
    (system-segment-descriptorbits-equiv-under-mask
         new-x x -4503599627370497)))