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Mxcsrbits

!mxcsrbits->reserved

Update the |X86ISA|::|RESERVED| field of a mxcsrbits bit structure.

Signature
(!mxcsrbits->reserved reserved x) → new-x
Arguments: reserved — Guard (16bits-p reserved).; x — Guard (mxcsrbits-p x).
Returns: new-x — Type (mxcsrbits-p new-x).

Definitions and Theorems

Function: !mxcsrbits->reserved$inline

(defun !mxcsrbits->reserved$inline (reserved x)
 (declare (xargs :guard (and (16bits-p reserved)
                             (mxcsrbits-p x))))
 (mbe :logic
      (b* ((reserved (mbe :logic (16bits-fix reserved)
                          :exec reserved))
           (x (mxcsrbits-fix x)))
        (part-install reserved x
                      :width 16
                      :low 16))
      :exec
      (the (unsigned-byte 32)
           (logior (the (unsigned-byte 32)
                        (logand (the (unsigned-byte 32) x)
                                (the (signed-byte 33) -4294901761)))
                   (the (unsigned-byte 32)
                        (ash (the (unsigned-byte 16) reserved)
                             16))))))

Theorem: mxcsrbits-p-of-!mxcsrbits->reserved

(defthm mxcsrbits-p-of-!mxcsrbits->reserved
  (b* ((new-x (!mxcsrbits->reserved$inline reserved x)))
    (mxcsrbits-p new-x))
  :rule-classes :rewrite)

Theorem: !mxcsrbits->reserved$inline-of-16bits-fix-reserved

(defthm !mxcsrbits->reserved$inline-of-16bits-fix-reserved
  (equal (!mxcsrbits->reserved$inline (16bits-fix reserved)
                                      x)
         (!mxcsrbits->reserved$inline reserved x)))

Theorem: !mxcsrbits->reserved$inline-16bits-equiv-congruence-on-reserved

(defthm
    !mxcsrbits->reserved$inline-16bits-equiv-congruence-on-reserved
  (implies (16bits-equiv reserved reserved-equiv)
           (equal (!mxcsrbits->reserved$inline reserved x)
                  (!mxcsrbits->reserved$inline reserved-equiv x)))
  :rule-classes :congruence)

Theorem: !mxcsrbits->reserved$inline-of-mxcsrbits-fix-x

(defthm !mxcsrbits->reserved$inline-of-mxcsrbits-fix-x
  (equal (!mxcsrbits->reserved$inline reserved (mxcsrbits-fix x))
         (!mxcsrbits->reserved$inline reserved x)))

Theorem: !mxcsrbits->reserved$inline-mxcsrbits-equiv-congruence-on-x

(defthm !mxcsrbits->reserved$inline-mxcsrbits-equiv-congruence-on-x
  (implies (mxcsrbits-equiv x x-equiv)
           (equal (!mxcsrbits->reserved$inline reserved x)
                  (!mxcsrbits->reserved$inline reserved x-equiv)))
  :rule-classes :congruence)

Theorem: !mxcsrbits->reserved-is-mxcsrbits

(defthm !mxcsrbits->reserved-is-mxcsrbits
  (equal (!mxcsrbits->reserved reserved x)
         (change-mxcsrbits x
                           :reserved reserved)))

Theorem: mxcsrbits->reserved-of-!mxcsrbits->reserved

(defthm mxcsrbits->reserved-of-!mxcsrbits->reserved
  (b* ((?new-x (!mxcsrbits->reserved$inline reserved x)))
    (equal (mxcsrbits->reserved new-x)
           (16bits-fix reserved))))

Theorem: !mxcsrbits->reserved-equiv-under-mask

(defthm !mxcsrbits->reserved-equiv-under-mask
  (b* ((?new-x (!mxcsrbits->reserved$inline reserved x)))
    (mxcsrbits-equiv-under-mask new-x x 65535)))