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Structures

Vex-prefixes-layout-structures

Functions to decode and collect VEX prefix bytes from an x86 instruction.

Definitions and Theorems

Function: vex-prefixes-p$inline

(defun vex-prefixes-p$inline (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p 24 x)
       :exec (and (natp x) (< x 16777216))))

Theorem: vex-prefixes-p-when-unsigned-byte-p

(defthm vex-prefixes-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 24 x)
           (vex-prefixes-p x)))

Theorem: unsigned-byte-p-when-vex-prefixes-p

(defthm unsigned-byte-p-when-vex-prefixes-p
  (implies (vex-prefixes-p x)
           (unsigned-byte-p 24 x)))

Theorem: vex-prefixes-p-compound-recognizer

(defthm vex-prefixes-p-compound-recognizer
  (implies (vex-prefixes-p x) (natp x))
  :rule-classes :compound-recognizer)

Function: vex-prefixes-fix$inline

(defun vex-prefixes-fix$inline (x)
  (declare (xargs :guard (vex-prefixes-p x)))
  (mbe :logic (loghead 24 x) :exec x))

Theorem: vex-prefixes-p-of-vex-prefixes-fix

(defthm vex-prefixes-p-of-vex-prefixes-fix
  (b* ((fty::fixed (vex-prefixes-fix$inline x)))
    (vex-prefixes-p fty::fixed))
  :rule-classes :rewrite)

Theorem: vex-prefixes-fix-when-vex-prefixes-p

(defthm vex-prefixes-fix-when-vex-prefixes-p
  (implies (vex-prefixes-p x)
           (equal (vex-prefixes-fix x) x)))

Function: vex-prefixes-equiv$inline

(defun vex-prefixes-equiv$inline (x y)
  (declare (xargs :guard (and (vex-prefixes-p x)
                              (vex-prefixes-p y))))
  (equal (vex-prefixes-fix x)
         (vex-prefixes-fix y)))

Theorem: vex-prefixes-equiv-is-an-equivalence

(defthm vex-prefixes-equiv-is-an-equivalence
  (and (booleanp (vex-prefixes-equiv x y))
       (vex-prefixes-equiv x x)
       (implies (vex-prefixes-equiv x y)
                (vex-prefixes-equiv y x))
       (implies (and (vex-prefixes-equiv x y)
                     (vex-prefixes-equiv y z))
                (vex-prefixes-equiv x z)))
  :rule-classes (:equivalence))

Theorem: vex-prefixes-equiv-implies-equal-vex-prefixes-fix-1

(defthm vex-prefixes-equiv-implies-equal-vex-prefixes-fix-1
  (implies (vex-prefixes-equiv x x-equiv)
           (equal (vex-prefixes-fix x)
                  (vex-prefixes-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vex-prefixes-fix-under-vex-prefixes-equiv

(defthm vex-prefixes-fix-under-vex-prefixes-equiv
  (vex-prefixes-equiv (vex-prefixes-fix x)
                      x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Function: vex-prefixes$inline

(defun vex-prefixes$inline (byte0 byte1 byte2)
  (declare (xargs :guard (and (8bits-p byte0)
                              (8bits-p byte1)
                              (8bits-p byte2))))
  (b* ((byte0 (mbe :logic (8bits-fix byte0)
                   :exec byte0))
       (byte1 (mbe :logic (8bits-fix byte1)
                   :exec byte1))
       (byte2 (mbe :logic (8bits-fix byte2)
                   :exec byte2)))
    (logapp 8 byte0 (logapp 8 byte1 byte2))))

Theorem: vex-prefixes-p-of-vex-prefixes

(defthm vex-prefixes-p-of-vex-prefixes
  (b* ((vex-prefixes (vex-prefixes$inline byte0 byte1 byte2)))
    (vex-prefixes-p vex-prefixes))
  :rule-classes :rewrite)

Theorem: vex-prefixes$inline-of-8bits-fix-byte0

(defthm vex-prefixes$inline-of-8bits-fix-byte0
  (equal (vex-prefixes$inline (8bits-fix byte0)
                              byte1 byte2)
         (vex-prefixes$inline byte0 byte1 byte2)))

Theorem: vex-prefixes$inline-8bits-equiv-congruence-on-byte0

(defthm vex-prefixes$inline-8bits-equiv-congruence-on-byte0
  (implies (8bits-equiv byte0 byte0-equiv)
           (equal (vex-prefixes$inline byte0 byte1 byte2)
                  (vex-prefixes$inline byte0-equiv byte1 byte2)))
  :rule-classes :congruence)

Theorem: vex-prefixes$inline-of-8bits-fix-byte1

(defthm vex-prefixes$inline-of-8bits-fix-byte1
  (equal (vex-prefixes$inline byte0 (8bits-fix byte1)
                              byte2)
         (vex-prefixes$inline byte0 byte1 byte2)))

Theorem: vex-prefixes$inline-8bits-equiv-congruence-on-byte1

(defthm vex-prefixes$inline-8bits-equiv-congruence-on-byte1
  (implies (8bits-equiv byte1 byte1-equiv)
           (equal (vex-prefixes$inline byte0 byte1 byte2)
                  (vex-prefixes$inline byte0 byte1-equiv byte2)))
  :rule-classes :congruence)

Theorem: vex-prefixes$inline-of-8bits-fix-byte2

(defthm vex-prefixes$inline-of-8bits-fix-byte2
  (equal (vex-prefixes$inline byte0 byte1 (8bits-fix byte2))
         (vex-prefixes$inline byte0 byte1 byte2)))

Theorem: vex-prefixes$inline-8bits-equiv-congruence-on-byte2

(defthm vex-prefixes$inline-8bits-equiv-congruence-on-byte2
  (implies (8bits-equiv byte2 byte2-equiv)
           (equal (vex-prefixes$inline byte0 byte1 byte2)
                  (vex-prefixes$inline byte0 byte1 byte2-equiv)))
  :rule-classes :congruence)

Function: vex-prefixes-equiv-under-mask$inline

(defun vex-prefixes-equiv-under-mask$inline (x x1 mask)
  (declare (xargs :guard (and (vex-prefixes-p x)
                              (vex-prefixes-p x1)
                              (integerp mask))))
  (fty::int-equiv-under-mask (vex-prefixes-fix x)
                             (vex-prefixes-fix x1)
                             mask))

Function: vex-prefixes->byte0$inline

(defun vex-prefixes->byte0$inline (x)
  (declare (xargs :guard (vex-prefixes-p x)))
  (mbe :logic
       (let ((x (vex-prefixes-fix x)))
         (part-select x :low 0 :width 8))
       :exec (the (unsigned-byte 8)
                  (logand (the (unsigned-byte 8) 255)
                          (the (unsigned-byte 24) x)))))

Theorem: 8bits-p-of-vex-prefixes->byte0

(defthm 8bits-p-of-vex-prefixes->byte0
  (b* ((byte0 (vex-prefixes->byte0$inline x)))
    (8bits-p byte0))
  :rule-classes :rewrite)

Theorem: vex-prefixes->byte0$inline-of-vex-prefixes-fix-x

(defthm vex-prefixes->byte0$inline-of-vex-prefixes-fix-x
  (equal (vex-prefixes->byte0$inline (vex-prefixes-fix x))
         (vex-prefixes->byte0$inline x)))

Theorem: vex-prefixes->byte0$inline-vex-prefixes-equiv-congruence-on-x

(defthm
      vex-prefixes->byte0$inline-vex-prefixes-equiv-congruence-on-x
  (implies (vex-prefixes-equiv x x-equiv)
           (equal (vex-prefixes->byte0$inline x)
                  (vex-prefixes->byte0$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex-prefixes->byte0-of-vex-prefixes

(defthm vex-prefixes->byte0-of-vex-prefixes
  (equal (vex-prefixes->byte0 (vex-prefixes byte0 byte1 byte2))
         (8bits-fix byte0)))

Theorem: vex-prefixes->byte0-of-write-with-mask

(defthm vex-prefixes->byte0-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex-prefixes-equiv-under-mask)
                (vex-prefixes-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 255)
                       0))
           (equal (vex-prefixes->byte0 x)
                  (vex-prefixes->byte0 y))))

Function: vex-prefixes->byte1$inline

(defun vex-prefixes->byte1$inline (x)
 (declare (xargs :guard (vex-prefixes-p x)))
 (mbe
    :logic
    (let ((x (vex-prefixes-fix x)))
      (part-select x :low 8 :width 8))
    :exec (the (unsigned-byte 8)
               (logand (the (unsigned-byte 8) 255)
                       (the (unsigned-byte 16)
                            (ash (the (unsigned-byte 24) x) -8))))))

Theorem: 8bits-p-of-vex-prefixes->byte1

(defthm 8bits-p-of-vex-prefixes->byte1
  (b* ((byte1 (vex-prefixes->byte1$inline x)))
    (8bits-p byte1))
  :rule-classes :rewrite)

Theorem: vex-prefixes->byte1$inline-of-vex-prefixes-fix-x

(defthm vex-prefixes->byte1$inline-of-vex-prefixes-fix-x
  (equal (vex-prefixes->byte1$inline (vex-prefixes-fix x))
         (vex-prefixes->byte1$inline x)))

Theorem: vex-prefixes->byte1$inline-vex-prefixes-equiv-congruence-on-x

(defthm
      vex-prefixes->byte1$inline-vex-prefixes-equiv-congruence-on-x
  (implies (vex-prefixes-equiv x x-equiv)
           (equal (vex-prefixes->byte1$inline x)
                  (vex-prefixes->byte1$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex-prefixes->byte1-of-vex-prefixes

(defthm vex-prefixes->byte1-of-vex-prefixes
  (equal (vex-prefixes->byte1 (vex-prefixes byte0 byte1 byte2))
         (8bits-fix byte1)))

Theorem: vex-prefixes->byte1-of-write-with-mask

(defthm vex-prefixes->byte1-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex-prefixes-equiv-under-mask)
                (vex-prefixes-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 65280)
                       0))
           (equal (vex-prefixes->byte1 x)
                  (vex-prefixes->byte1 y))))

Function: vex-prefixes->byte2$inline

(defun vex-prefixes->byte2$inline (x)
  (declare (xargs :guard (vex-prefixes-p x)))
  (mbe :logic
       (let ((x (vex-prefixes-fix x)))
         (part-select x :low 16 :width 8))
       :exec (the (unsigned-byte 8)
                  (logand (the (unsigned-byte 8) 255)
                          (the (unsigned-byte 8)
                               (ash (the (unsigned-byte 24) x)
                                    -16))))))

Theorem: 8bits-p-of-vex-prefixes->byte2

(defthm 8bits-p-of-vex-prefixes->byte2
  (b* ((byte2 (vex-prefixes->byte2$inline x)))
    (8bits-p byte2))
  :rule-classes :rewrite)

Theorem: vex-prefixes->byte2$inline-of-vex-prefixes-fix-x

(defthm vex-prefixes->byte2$inline-of-vex-prefixes-fix-x
  (equal (vex-prefixes->byte2$inline (vex-prefixes-fix x))
         (vex-prefixes->byte2$inline x)))

Theorem: vex-prefixes->byte2$inline-vex-prefixes-equiv-congruence-on-x

(defthm
      vex-prefixes->byte2$inline-vex-prefixes-equiv-congruence-on-x
  (implies (vex-prefixes-equiv x x-equiv)
           (equal (vex-prefixes->byte2$inline x)
                  (vex-prefixes->byte2$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex-prefixes->byte2-of-vex-prefixes

(defthm vex-prefixes->byte2-of-vex-prefixes
  (equal (vex-prefixes->byte2 (vex-prefixes byte0 byte1 byte2))
         (8bits-fix byte2)))

Theorem: vex-prefixes->byte2-of-write-with-mask

(defthm vex-prefixes->byte2-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex-prefixes-equiv-under-mask)
                (vex-prefixes-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 16711680)
                       0))
           (equal (vex-prefixes->byte2 x)
                  (vex-prefixes->byte2 y))))

Theorem: vex-prefixes-fix-in-terms-of-vex-prefixes

(defthm vex-prefixes-fix-in-terms-of-vex-prefixes
  (equal (vex-prefixes-fix x)
         (change-vex-prefixes x)))

Function: !vex-prefixes->byte0$inline

(defun !vex-prefixes->byte0$inline (byte0 x)
  (declare (xargs :guard (and (8bits-p byte0)
                              (vex-prefixes-p x))))
  (mbe :logic
       (b* ((byte0 (mbe :logic (8bits-fix byte0)
                        :exec byte0))
            (x (vex-prefixes-fix x)))
         (part-install byte0 x :width 8 :low 0))
       :exec (the (unsigned-byte 24)
                  (logior (the (unsigned-byte 24)
                               (logand (the (unsigned-byte 24) x)
                                       (the (signed-byte 9) -256)))
                          (the (unsigned-byte 8) byte0)))))

Theorem: vex-prefixes-p-of-!vex-prefixes->byte0

(defthm vex-prefixes-p-of-!vex-prefixes->byte0
  (b* ((new-x (!vex-prefixes->byte0$inline byte0 x)))
    (vex-prefixes-p new-x))
  :rule-classes :rewrite)

Theorem: !vex-prefixes->byte0$inline-of-8bits-fix-byte0

(defthm !vex-prefixes->byte0$inline-of-8bits-fix-byte0
  (equal (!vex-prefixes->byte0$inline (8bits-fix byte0)
                                      x)
         (!vex-prefixes->byte0$inline byte0 x)))

Theorem: !vex-prefixes->byte0$inline-8bits-equiv-congruence-on-byte0

(defthm !vex-prefixes->byte0$inline-8bits-equiv-congruence-on-byte0
  (implies (8bits-equiv byte0 byte0-equiv)
           (equal (!vex-prefixes->byte0$inline byte0 x)
                  (!vex-prefixes->byte0$inline byte0-equiv x)))
  :rule-classes :congruence)

Theorem: !vex-prefixes->byte0$inline-of-vex-prefixes-fix-x

(defthm !vex-prefixes->byte0$inline-of-vex-prefixes-fix-x
  (equal (!vex-prefixes->byte0$inline byte0 (vex-prefixes-fix x))
         (!vex-prefixes->byte0$inline byte0 x)))

Theorem: !vex-prefixes->byte0$inline-vex-prefixes-equiv-congruence-on-x

(defthm
     !vex-prefixes->byte0$inline-vex-prefixes-equiv-congruence-on-x
  (implies (vex-prefixes-equiv x x-equiv)
           (equal (!vex-prefixes->byte0$inline byte0 x)
                  (!vex-prefixes->byte0$inline byte0 x-equiv)))
  :rule-classes :congruence)

Theorem: !vex-prefixes->byte0-is-vex-prefixes

(defthm !vex-prefixes->byte0-is-vex-prefixes
  (equal (!vex-prefixes->byte0 byte0 x)
         (change-vex-prefixes x :byte0 byte0)))

Theorem: vex-prefixes->byte0-of-!vex-prefixes->byte0

(defthm vex-prefixes->byte0-of-!vex-prefixes->byte0
  (b* ((?new-x (!vex-prefixes->byte0$inline byte0 x)))
    (equal (vex-prefixes->byte0 new-x)
           (8bits-fix byte0))))

Theorem: !vex-prefixes->byte0-equiv-under-mask

(defthm !vex-prefixes->byte0-equiv-under-mask
  (b* ((?new-x (!vex-prefixes->byte0$inline byte0 x)))
    (vex-prefixes-equiv-under-mask new-x x -256)))

Function: !vex-prefixes->byte1$inline

(defun !vex-prefixes->byte1$inline (byte1 x)
 (declare (xargs :guard (and (8bits-p byte1)
                             (vex-prefixes-p x))))
 (mbe
     :logic
     (b* ((byte1 (mbe :logic (8bits-fix byte1)
                      :exec byte1))
          (x (vex-prefixes-fix x)))
       (part-install byte1 x :width 8 :low 8))
     :exec (the (unsigned-byte 24)
                (logior (the (unsigned-byte 24)
                             (logand (the (unsigned-byte 24) x)
                                     (the (signed-byte 17) -65281)))
                        (the (unsigned-byte 16)
                             (ash (the (unsigned-byte 8) byte1)
                                  8))))))

Theorem: vex-prefixes-p-of-!vex-prefixes->byte1

(defthm vex-prefixes-p-of-!vex-prefixes->byte1
  (b* ((new-x (!vex-prefixes->byte1$inline byte1 x)))
    (vex-prefixes-p new-x))
  :rule-classes :rewrite)

Theorem: !vex-prefixes->byte1$inline-of-8bits-fix-byte1

(defthm !vex-prefixes->byte1$inline-of-8bits-fix-byte1
  (equal (!vex-prefixes->byte1$inline (8bits-fix byte1)
                                      x)
         (!vex-prefixes->byte1$inline byte1 x)))

Theorem: !vex-prefixes->byte1$inline-8bits-equiv-congruence-on-byte1

(defthm !vex-prefixes->byte1$inline-8bits-equiv-congruence-on-byte1
  (implies (8bits-equiv byte1 byte1-equiv)
           (equal (!vex-prefixes->byte1$inline byte1 x)
                  (!vex-prefixes->byte1$inline byte1-equiv x)))
  :rule-classes :congruence)

Theorem: !vex-prefixes->byte1$inline-of-vex-prefixes-fix-x

(defthm !vex-prefixes->byte1$inline-of-vex-prefixes-fix-x
  (equal (!vex-prefixes->byte1$inline byte1 (vex-prefixes-fix x))
         (!vex-prefixes->byte1$inline byte1 x)))

Theorem: !vex-prefixes->byte1$inline-vex-prefixes-equiv-congruence-on-x

(defthm
     !vex-prefixes->byte1$inline-vex-prefixes-equiv-congruence-on-x
  (implies (vex-prefixes-equiv x x-equiv)
           (equal (!vex-prefixes->byte1$inline byte1 x)
                  (!vex-prefixes->byte1$inline byte1 x-equiv)))
  :rule-classes :congruence)

Theorem: !vex-prefixes->byte1-is-vex-prefixes

(defthm !vex-prefixes->byte1-is-vex-prefixes
  (equal (!vex-prefixes->byte1 byte1 x)
         (change-vex-prefixes x :byte1 byte1)))

Theorem: vex-prefixes->byte1-of-!vex-prefixes->byte1

(defthm vex-prefixes->byte1-of-!vex-prefixes->byte1
  (b* ((?new-x (!vex-prefixes->byte1$inline byte1 x)))
    (equal (vex-prefixes->byte1 new-x)
           (8bits-fix byte1))))

Theorem: !vex-prefixes->byte1-equiv-under-mask

(defthm !vex-prefixes->byte1-equiv-under-mask
  (b* ((?new-x (!vex-prefixes->byte1$inline byte1 x)))
    (vex-prefixes-equiv-under-mask new-x x -65281)))

Function: !vex-prefixes->byte2$inline

(defun !vex-prefixes->byte2$inline (byte2 x)
 (declare (xargs :guard (and (8bits-p byte2)
                             (vex-prefixes-p x))))
 (mbe
  :logic
  (b* ((byte2 (mbe :logic (8bits-fix byte2)
                   :exec byte2))
       (x (vex-prefixes-fix x)))
    (part-install byte2 x :width 8 :low 16))
  :exec (the (unsigned-byte 24)
             (logior (the (unsigned-byte 24)
                          (logand (the (unsigned-byte 24) x)
                                  (the (signed-byte 25) -16711681)))
                     (the (unsigned-byte 24)
                          (ash (the (unsigned-byte 8) byte2)
                               16))))))

Theorem: vex-prefixes-p-of-!vex-prefixes->byte2

(defthm vex-prefixes-p-of-!vex-prefixes->byte2
  (b* ((new-x (!vex-prefixes->byte2$inline byte2 x)))
    (vex-prefixes-p new-x))
  :rule-classes :rewrite)

Theorem: !vex-prefixes->byte2$inline-of-8bits-fix-byte2

(defthm !vex-prefixes->byte2$inline-of-8bits-fix-byte2
  (equal (!vex-prefixes->byte2$inline (8bits-fix byte2)
                                      x)
         (!vex-prefixes->byte2$inline byte2 x)))

Theorem: !vex-prefixes->byte2$inline-8bits-equiv-congruence-on-byte2

(defthm !vex-prefixes->byte2$inline-8bits-equiv-congruence-on-byte2
  (implies (8bits-equiv byte2 byte2-equiv)
           (equal (!vex-prefixes->byte2$inline byte2 x)
                  (!vex-prefixes->byte2$inline byte2-equiv x)))
  :rule-classes :congruence)

Theorem: !vex-prefixes->byte2$inline-of-vex-prefixes-fix-x

(defthm !vex-prefixes->byte2$inline-of-vex-prefixes-fix-x
  (equal (!vex-prefixes->byte2$inline byte2 (vex-prefixes-fix x))
         (!vex-prefixes->byte2$inline byte2 x)))

Theorem: !vex-prefixes->byte2$inline-vex-prefixes-equiv-congruence-on-x

(defthm
     !vex-prefixes->byte2$inline-vex-prefixes-equiv-congruence-on-x
  (implies (vex-prefixes-equiv x x-equiv)
           (equal (!vex-prefixes->byte2$inline byte2 x)
                  (!vex-prefixes->byte2$inline byte2 x-equiv)))
  :rule-classes :congruence)

Theorem: !vex-prefixes->byte2-is-vex-prefixes

(defthm !vex-prefixes->byte2-is-vex-prefixes
  (equal (!vex-prefixes->byte2 byte2 x)
         (change-vex-prefixes x :byte2 byte2)))

Theorem: vex-prefixes->byte2-of-!vex-prefixes->byte2

(defthm vex-prefixes->byte2-of-!vex-prefixes->byte2
  (b* ((?new-x (!vex-prefixes->byte2$inline byte2 x)))
    (equal (vex-prefixes->byte2 new-x)
           (8bits-fix byte2))))

Theorem: !vex-prefixes->byte2-equiv-under-mask

(defthm !vex-prefixes->byte2-equiv-under-mask
  (b* ((?new-x (!vex-prefixes->byte2$inline byte2 x)))
    (vex-prefixes-equiv-under-mask new-x x 65535)))

Function: vex-prefixes-debug$inline

(defun vex-prefixes-debug$inline (x)
  (declare (xargs :guard (vex-prefixes-p x)))
  (b* (((vex-prefixes x)))
    (cons (cons 'byte0 x.byte0)
          (cons (cons 'byte1 x.byte1)
                (cons (cons 'byte2 x.byte2) nil)))))

Function: vex-prefixes-byte0-p$inline

(defun vex-prefixes-byte0-p$inline (vex-prefixes)
  (declare (xargs :guard (vex-prefixes-p vex-prefixes)))
  (let ((byte0 (vex-prefixes->byte0 vex-prefixes)))
    (or (equal byte0 197)
        (equal byte0 196))))

Theorem: booleanp-of-vex-prefixes-byte0-p

(defthm booleanp-of-vex-prefixes-byte0-p
  (b* ((ok (vex-prefixes-byte0-p$inline vex-prefixes)))
    (booleanp ok))
  :rule-classes :rewrite)

Function: vex2-byte1-p$inline

(defun vex2-byte1-p$inline (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p 8 x)
       :exec (and (natp x) (< x 256))))

Theorem: vex2-byte1-p-when-unsigned-byte-p

(defthm vex2-byte1-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 8 x)
           (vex2-byte1-p x)))

Theorem: unsigned-byte-p-when-vex2-byte1-p

(defthm unsigned-byte-p-when-vex2-byte1-p
  (implies (vex2-byte1-p x)
           (unsigned-byte-p 8 x)))

Theorem: vex2-byte1-p-compound-recognizer

(defthm vex2-byte1-p-compound-recognizer
  (implies (vex2-byte1-p x) (natp x))
  :rule-classes :compound-recognizer)

Function: vex2-byte1-fix$inline

(defun vex2-byte1-fix$inline (x)
  (declare (xargs :guard (vex2-byte1-p x)))
  (mbe :logic (loghead 8 x) :exec x))

Theorem: vex2-byte1-p-of-vex2-byte1-fix

(defthm vex2-byte1-p-of-vex2-byte1-fix
  (b* ((fty::fixed (vex2-byte1-fix$inline x)))
    (vex2-byte1-p fty::fixed))
  :rule-classes :rewrite)

Theorem: vex2-byte1-fix-when-vex2-byte1-p

(defthm vex2-byte1-fix-when-vex2-byte1-p
  (implies (vex2-byte1-p x)
           (equal (vex2-byte1-fix x) x)))

Function: vex2-byte1-equiv$inline

(defun vex2-byte1-equiv$inline (x y)
  (declare (xargs :guard (and (vex2-byte1-p x)
                              (vex2-byte1-p y))))
  (equal (vex2-byte1-fix x)
         (vex2-byte1-fix y)))

Theorem: vex2-byte1-equiv-is-an-equivalence

(defthm vex2-byte1-equiv-is-an-equivalence
  (and (booleanp (vex2-byte1-equiv x y))
       (vex2-byte1-equiv x x)
       (implies (vex2-byte1-equiv x y)
                (vex2-byte1-equiv y x))
       (implies (and (vex2-byte1-equiv x y)
                     (vex2-byte1-equiv y z))
                (vex2-byte1-equiv x z)))
  :rule-classes (:equivalence))

Theorem: vex2-byte1-equiv-implies-equal-vex2-byte1-fix-1

(defthm vex2-byte1-equiv-implies-equal-vex2-byte1-fix-1
  (implies (vex2-byte1-equiv x x-equiv)
           (equal (vex2-byte1-fix x)
                  (vex2-byte1-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vex2-byte1-fix-under-vex2-byte1-equiv

(defthm vex2-byte1-fix-under-vex2-byte1-equiv
  (vex2-byte1-equiv (vex2-byte1-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Function: vex2-byte1$inline

(defun vex2-byte1$inline (pp l vvvv r)
  (declare (xargs :guard (and (2bits-p pp)
                              (bitp l)
                              (4bits-p vvvv)
                              (bitp r))))
  (b* ((pp (mbe :logic (2bits-fix pp) :exec pp))
       (l (mbe :logic (bfix l) :exec l))
       (vvvv (mbe :logic (4bits-fix vvvv)
                  :exec vvvv))
       (r (mbe :logic (bfix r) :exec r)))
    (logapp 2 pp (logapp 1 l (logapp 4 vvvv r)))))

Theorem: vex2-byte1-p-of-vex2-byte1

(defthm vex2-byte1-p-of-vex2-byte1
  (b* ((vex2-byte1 (vex2-byte1$inline pp l vvvv r)))
    (vex2-byte1-p vex2-byte1))
  :rule-classes :rewrite)

Theorem: vex2-byte1$inline-of-2bits-fix-pp

(defthm vex2-byte1$inline-of-2bits-fix-pp
  (equal (vex2-byte1$inline (2bits-fix pp)
                            l vvvv r)
         (vex2-byte1$inline pp l vvvv r)))

Theorem: vex2-byte1$inline-2bits-equiv-congruence-on-pp

(defthm vex2-byte1$inline-2bits-equiv-congruence-on-pp
  (implies (2bits-equiv pp pp-equiv)
           (equal (vex2-byte1$inline pp l vvvv r)
                  (vex2-byte1$inline pp-equiv l vvvv r)))
  :rule-classes :congruence)

Theorem: vex2-byte1$inline-of-bfix-l

(defthm vex2-byte1$inline-of-bfix-l
  (equal (vex2-byte1$inline pp (bfix l) vvvv r)
         (vex2-byte1$inline pp l vvvv r)))

Theorem: vex2-byte1$inline-bit-equiv-congruence-on-l

(defthm vex2-byte1$inline-bit-equiv-congruence-on-l
  (implies (bit-equiv l l-equiv)
           (equal (vex2-byte1$inline pp l vvvv r)
                  (vex2-byte1$inline pp l-equiv vvvv r)))
  :rule-classes :congruence)

Theorem: vex2-byte1$inline-of-4bits-fix-vvvv

(defthm vex2-byte1$inline-of-4bits-fix-vvvv
  (equal (vex2-byte1$inline pp l (4bits-fix vvvv)
                            r)
         (vex2-byte1$inline pp l vvvv r)))

Theorem: vex2-byte1$inline-4bits-equiv-congruence-on-vvvv

(defthm vex2-byte1$inline-4bits-equiv-congruence-on-vvvv
  (implies (4bits-equiv vvvv vvvv-equiv)
           (equal (vex2-byte1$inline pp l vvvv r)
                  (vex2-byte1$inline pp l vvvv-equiv r)))
  :rule-classes :congruence)

Theorem: vex2-byte1$inline-of-bfix-r

(defthm vex2-byte1$inline-of-bfix-r
  (equal (vex2-byte1$inline pp l vvvv (bfix r))
         (vex2-byte1$inline pp l vvvv r)))

Theorem: vex2-byte1$inline-bit-equiv-congruence-on-r

(defthm vex2-byte1$inline-bit-equiv-congruence-on-r
  (implies (bit-equiv r r-equiv)
           (equal (vex2-byte1$inline pp l vvvv r)
                  (vex2-byte1$inline pp l vvvv r-equiv)))
  :rule-classes :congruence)

Function: vex2-byte1-equiv-under-mask$inline

(defun vex2-byte1-equiv-under-mask$inline (x x1 mask)
  (declare (xargs :guard (and (vex2-byte1-p x)
                              (vex2-byte1-p x1)
                              (integerp mask))))
  (fty::int-equiv-under-mask (vex2-byte1-fix x)
                             (vex2-byte1-fix x1)
                             mask))

Function: vex2-byte1->pp$inline

(defun vex2-byte1->pp$inline (x)
  (declare (xargs :guard (vex2-byte1-p x)))
  (mbe :logic
       (let ((x (vex2-byte1-fix x)))
         (part-select x :low 0 :width 2))
       :exec (the (unsigned-byte 2)
                  (logand (the (unsigned-byte 2) 3)
                          (the (unsigned-byte 8) x)))))

Theorem: 2bits-p-of-vex2-byte1->pp

(defthm 2bits-p-of-vex2-byte1->pp
  (b* ((pp (vex2-byte1->pp$inline x)))
    (2bits-p pp))
  :rule-classes :rewrite)

Theorem: vex2-byte1->pp$inline-of-vex2-byte1-fix-x

(defthm vex2-byte1->pp$inline-of-vex2-byte1-fix-x
  (equal (vex2-byte1->pp$inline (vex2-byte1-fix x))
         (vex2-byte1->pp$inline x)))

Theorem: vex2-byte1->pp$inline-vex2-byte1-equiv-congruence-on-x

(defthm vex2-byte1->pp$inline-vex2-byte1-equiv-congruence-on-x
  (implies (vex2-byte1-equiv x x-equiv)
           (equal (vex2-byte1->pp$inline x)
                  (vex2-byte1->pp$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex2-byte1->pp-of-vex2-byte1

(defthm vex2-byte1->pp-of-vex2-byte1
  (equal (vex2-byte1->pp (vex2-byte1 pp l vvvv r))
         (2bits-fix pp)))

Theorem: vex2-byte1->pp-of-write-with-mask

(defthm vex2-byte1->pp-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex2-byte1-equiv-under-mask)
                (vex2-byte1-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 3) 0))
           (equal (vex2-byte1->pp x)
                  (vex2-byte1->pp y))))

Function: vex2-byte1->l$inline

(defun vex2-byte1->l$inline (x)
 (declare (xargs :guard (vex2-byte1-p x)))
 (mbe
     :logic
     (let ((x (vex2-byte1-fix x)))
       (part-select x :low 2 :width 1))
     :exec (the (unsigned-byte 1)
                (logand (the (unsigned-byte 1) 1)
                        (the (unsigned-byte 6)
                             (ash (the (unsigned-byte 8) x) -2))))))

Theorem: bitp-of-vex2-byte1->l

(defthm bitp-of-vex2-byte1->l
  (b* ((l (vex2-byte1->l$inline x)))
    (bitp l))
  :rule-classes :rewrite)

Theorem: vex2-byte1->l$inline-of-vex2-byte1-fix-x

(defthm vex2-byte1->l$inline-of-vex2-byte1-fix-x
  (equal (vex2-byte1->l$inline (vex2-byte1-fix x))
         (vex2-byte1->l$inline x)))

Theorem: vex2-byte1->l$inline-vex2-byte1-equiv-congruence-on-x

(defthm vex2-byte1->l$inline-vex2-byte1-equiv-congruence-on-x
  (implies (vex2-byte1-equiv x x-equiv)
           (equal (vex2-byte1->l$inline x)
                  (vex2-byte1->l$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex2-byte1->l-of-vex2-byte1

(defthm vex2-byte1->l-of-vex2-byte1
  (equal (vex2-byte1->l (vex2-byte1 pp l vvvv r))
         (bfix l)))

Theorem: vex2-byte1->l-of-write-with-mask

(defthm vex2-byte1->l-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex2-byte1-equiv-under-mask)
                (vex2-byte1-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 4) 0))
           (equal (vex2-byte1->l x)
                  (vex2-byte1->l y))))

Function: vex2-byte1->vvvv$inline

(defun vex2-byte1->vvvv$inline (x)
 (declare (xargs :guard (vex2-byte1-p x)))
 (mbe
     :logic
     (let ((x (vex2-byte1-fix x)))
       (part-select x :low 3 :width 4))
     :exec (the (unsigned-byte 4)
                (logand (the (unsigned-byte 4) 15)
                        (the (unsigned-byte 5)
                             (ash (the (unsigned-byte 8) x) -3))))))

Theorem: 4bits-p-of-vex2-byte1->vvvv

(defthm 4bits-p-of-vex2-byte1->vvvv
  (b* ((vvvv (vex2-byte1->vvvv$inline x)))
    (4bits-p vvvv))
  :rule-classes :rewrite)

Theorem: vex2-byte1->vvvv$inline-of-vex2-byte1-fix-x

(defthm vex2-byte1->vvvv$inline-of-vex2-byte1-fix-x
  (equal (vex2-byte1->vvvv$inline (vex2-byte1-fix x))
         (vex2-byte1->vvvv$inline x)))

Theorem: vex2-byte1->vvvv$inline-vex2-byte1-equiv-congruence-on-x

(defthm vex2-byte1->vvvv$inline-vex2-byte1-equiv-congruence-on-x
  (implies (vex2-byte1-equiv x x-equiv)
           (equal (vex2-byte1->vvvv$inline x)
                  (vex2-byte1->vvvv$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex2-byte1->vvvv-of-vex2-byte1

(defthm vex2-byte1->vvvv-of-vex2-byte1
  (equal (vex2-byte1->vvvv (vex2-byte1 pp l vvvv r))
         (4bits-fix vvvv)))

Theorem: vex2-byte1->vvvv-of-write-with-mask

(defthm vex2-byte1->vvvv-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex2-byte1-equiv-under-mask)
                (vex2-byte1-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 120)
                       0))
           (equal (vex2-byte1->vvvv x)
                  (vex2-byte1->vvvv y))))

Function: vex2-byte1->r$inline

(defun vex2-byte1->r$inline (x)
 (declare (xargs :guard (vex2-byte1-p x)))
 (mbe
     :logic
     (let ((x (vex2-byte1-fix x)))
       (part-select x :low 7 :width 1))
     :exec (the (unsigned-byte 1)
                (logand (the (unsigned-byte 1) 1)
                        (the (unsigned-byte 1)
                             (ash (the (unsigned-byte 8) x) -7))))))

Theorem: bitp-of-vex2-byte1->r

(defthm bitp-of-vex2-byte1->r
  (b* ((r (vex2-byte1->r$inline x)))
    (bitp r))
  :rule-classes :rewrite)

Theorem: vex2-byte1->r$inline-of-vex2-byte1-fix-x

(defthm vex2-byte1->r$inline-of-vex2-byte1-fix-x
  (equal (vex2-byte1->r$inline (vex2-byte1-fix x))
         (vex2-byte1->r$inline x)))

Theorem: vex2-byte1->r$inline-vex2-byte1-equiv-congruence-on-x

(defthm vex2-byte1->r$inline-vex2-byte1-equiv-congruence-on-x
  (implies (vex2-byte1-equiv x x-equiv)
           (equal (vex2-byte1->r$inline x)
                  (vex2-byte1->r$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex2-byte1->r-of-vex2-byte1

(defthm vex2-byte1->r-of-vex2-byte1
  (equal (vex2-byte1->r (vex2-byte1 pp l vvvv r))
         (bfix r)))

Theorem: vex2-byte1->r-of-write-with-mask

(defthm vex2-byte1->r-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex2-byte1-equiv-under-mask)
                (vex2-byte1-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 128)
                       0))
           (equal (vex2-byte1->r x)
                  (vex2-byte1->r y))))

Theorem: vex2-byte1-fix-in-terms-of-vex2-byte1

(defthm vex2-byte1-fix-in-terms-of-vex2-byte1
  (equal (vex2-byte1-fix x)
         (change-vex2-byte1 x)))

Function: !vex2-byte1->pp$inline

(defun !vex2-byte1->pp$inline (pp x)
  (declare (xargs :guard (and (2bits-p pp) (vex2-byte1-p x))))
  (mbe :logic
       (b* ((pp (mbe :logic (2bits-fix pp) :exec pp))
            (x (vex2-byte1-fix x)))
         (part-install pp x :width 2 :low 0))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 3) -4)))
                          (the (unsigned-byte 2) pp)))))

Theorem: vex2-byte1-p-of-!vex2-byte1->pp

(defthm vex2-byte1-p-of-!vex2-byte1->pp
  (b* ((new-x (!vex2-byte1->pp$inline pp x)))
    (vex2-byte1-p new-x))
  :rule-classes :rewrite)

Theorem: !vex2-byte1->pp$inline-of-2bits-fix-pp

(defthm !vex2-byte1->pp$inline-of-2bits-fix-pp
  (equal (!vex2-byte1->pp$inline (2bits-fix pp)
                                 x)
         (!vex2-byte1->pp$inline pp x)))

Theorem: !vex2-byte1->pp$inline-2bits-equiv-congruence-on-pp

(defthm !vex2-byte1->pp$inline-2bits-equiv-congruence-on-pp
  (implies (2bits-equiv pp pp-equiv)
           (equal (!vex2-byte1->pp$inline pp x)
                  (!vex2-byte1->pp$inline pp-equiv x)))
  :rule-classes :congruence)

Theorem: !vex2-byte1->pp$inline-of-vex2-byte1-fix-x

(defthm !vex2-byte1->pp$inline-of-vex2-byte1-fix-x
  (equal (!vex2-byte1->pp$inline pp (vex2-byte1-fix x))
         (!vex2-byte1->pp$inline pp x)))

Theorem: !vex2-byte1->pp$inline-vex2-byte1-equiv-congruence-on-x

(defthm !vex2-byte1->pp$inline-vex2-byte1-equiv-congruence-on-x
  (implies (vex2-byte1-equiv x x-equiv)
           (equal (!vex2-byte1->pp$inline pp x)
                  (!vex2-byte1->pp$inline pp x-equiv)))
  :rule-classes :congruence)

Theorem: !vex2-byte1->pp-is-vex2-byte1

(defthm !vex2-byte1->pp-is-vex2-byte1
  (equal (!vex2-byte1->pp pp x)
         (change-vex2-byte1 x :pp pp)))

Theorem: vex2-byte1->pp-of-!vex2-byte1->pp

(defthm vex2-byte1->pp-of-!vex2-byte1->pp
  (b* ((?new-x (!vex2-byte1->pp$inline pp x)))
    (equal (vex2-byte1->pp new-x)
           (2bits-fix pp))))

Theorem: !vex2-byte1->pp-equiv-under-mask

(defthm !vex2-byte1->pp-equiv-under-mask
  (b* ((?new-x (!vex2-byte1->pp$inline pp x)))
    (vex2-byte1-equiv-under-mask new-x x -4)))

Function: !vex2-byte1->l$inline

(defun !vex2-byte1->l$inline (l x)
 (declare (xargs :guard (and (bitp l) (vex2-byte1-p x))))
 (mbe :logic
      (b* ((l (mbe :logic (bfix l) :exec l))
           (x (vex2-byte1-fix x)))
        (part-install l x :width 1 :low 2))
      :exec (the (unsigned-byte 8)
                 (logior (the (unsigned-byte 8)
                              (logand (the (unsigned-byte 8) x)
                                      (the (signed-byte 4) -5)))
                         (the (unsigned-byte 3)
                              (ash (the (unsigned-byte 1) l) 2))))))

Theorem: vex2-byte1-p-of-!vex2-byte1->l

(defthm vex2-byte1-p-of-!vex2-byte1->l
  (b* ((new-x (!vex2-byte1->l$inline l x)))
    (vex2-byte1-p new-x))
  :rule-classes :rewrite)

Theorem: !vex2-byte1->l$inline-of-bfix-l

(defthm !vex2-byte1->l$inline-of-bfix-l
  (equal (!vex2-byte1->l$inline (bfix l) x)
         (!vex2-byte1->l$inline l x)))

Theorem: !vex2-byte1->l$inline-bit-equiv-congruence-on-l

(defthm !vex2-byte1->l$inline-bit-equiv-congruence-on-l
  (implies (bit-equiv l l-equiv)
           (equal (!vex2-byte1->l$inline l x)
                  (!vex2-byte1->l$inline l-equiv x)))
  :rule-classes :congruence)

Theorem: !vex2-byte1->l$inline-of-vex2-byte1-fix-x

(defthm !vex2-byte1->l$inline-of-vex2-byte1-fix-x
  (equal (!vex2-byte1->l$inline l (vex2-byte1-fix x))
         (!vex2-byte1->l$inline l x)))

Theorem: !vex2-byte1->l$inline-vex2-byte1-equiv-congruence-on-x

(defthm !vex2-byte1->l$inline-vex2-byte1-equiv-congruence-on-x
  (implies (vex2-byte1-equiv x x-equiv)
           (equal (!vex2-byte1->l$inline l x)
                  (!vex2-byte1->l$inline l x-equiv)))
  :rule-classes :congruence)

Theorem: !vex2-byte1->l-is-vex2-byte1

(defthm !vex2-byte1->l-is-vex2-byte1
  (equal (!vex2-byte1->l l x)
         (change-vex2-byte1 x :l l)))

Theorem: vex2-byte1->l-of-!vex2-byte1->l

(defthm vex2-byte1->l-of-!vex2-byte1->l
  (b* ((?new-x (!vex2-byte1->l$inline l x)))
    (equal (vex2-byte1->l new-x) (bfix l))))

Theorem: !vex2-byte1->l-equiv-under-mask

(defthm !vex2-byte1->l-equiv-under-mask
  (b* ((?new-x (!vex2-byte1->l$inline l x)))
    (vex2-byte1-equiv-under-mask new-x x -5)))

Function: !vex2-byte1->vvvv$inline

(defun !vex2-byte1->vvvv$inline (vvvv x)
  (declare (xargs :guard (and (4bits-p vvvv) (vex2-byte1-p x))))
  (mbe :logic
       (b* ((vvvv (mbe :logic (4bits-fix vvvv)
                       :exec vvvv))
            (x (vex2-byte1-fix x)))
         (part-install vvvv x :width 4 :low 3))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 8) -121)))
                          (the (unsigned-byte 7)
                               (ash (the (unsigned-byte 4) vvvv)
                                    3))))))

Theorem: vex2-byte1-p-of-!vex2-byte1->vvvv

(defthm vex2-byte1-p-of-!vex2-byte1->vvvv
  (b* ((new-x (!vex2-byte1->vvvv$inline vvvv x)))
    (vex2-byte1-p new-x))
  :rule-classes :rewrite)

Theorem: !vex2-byte1->vvvv$inline-of-4bits-fix-vvvv

(defthm !vex2-byte1->vvvv$inline-of-4bits-fix-vvvv
  (equal (!vex2-byte1->vvvv$inline (4bits-fix vvvv)
                                   x)
         (!vex2-byte1->vvvv$inline vvvv x)))

Theorem: !vex2-byte1->vvvv$inline-4bits-equiv-congruence-on-vvvv

(defthm !vex2-byte1->vvvv$inline-4bits-equiv-congruence-on-vvvv
  (implies (4bits-equiv vvvv vvvv-equiv)
           (equal (!vex2-byte1->vvvv$inline vvvv x)
                  (!vex2-byte1->vvvv$inline vvvv-equiv x)))
  :rule-classes :congruence)

Theorem: !vex2-byte1->vvvv$inline-of-vex2-byte1-fix-x

(defthm !vex2-byte1->vvvv$inline-of-vex2-byte1-fix-x
  (equal (!vex2-byte1->vvvv$inline vvvv (vex2-byte1-fix x))
         (!vex2-byte1->vvvv$inline vvvv x)))

Theorem: !vex2-byte1->vvvv$inline-vex2-byte1-equiv-congruence-on-x

(defthm !vex2-byte1->vvvv$inline-vex2-byte1-equiv-congruence-on-x
  (implies (vex2-byte1-equiv x x-equiv)
           (equal (!vex2-byte1->vvvv$inline vvvv x)
                  (!vex2-byte1->vvvv$inline vvvv x-equiv)))
  :rule-classes :congruence)

Theorem: !vex2-byte1->vvvv-is-vex2-byte1

(defthm !vex2-byte1->vvvv-is-vex2-byte1
  (equal (!vex2-byte1->vvvv vvvv x)
         (change-vex2-byte1 x :vvvv vvvv)))

Theorem: vex2-byte1->vvvv-of-!vex2-byte1->vvvv

(defthm vex2-byte1->vvvv-of-!vex2-byte1->vvvv
  (b* ((?new-x (!vex2-byte1->vvvv$inline vvvv x)))
    (equal (vex2-byte1->vvvv new-x)
           (4bits-fix vvvv))))

Theorem: !vex2-byte1->vvvv-equiv-under-mask

(defthm !vex2-byte1->vvvv-equiv-under-mask
  (b* ((?new-x (!vex2-byte1->vvvv$inline vvvv x)))
    (vex2-byte1-equiv-under-mask new-x x -121)))

Function: !vex2-byte1->r$inline

(defun !vex2-byte1->r$inline (r x)
 (declare (xargs :guard (and (bitp r) (vex2-byte1-p x))))
 (mbe :logic
      (b* ((r (mbe :logic (bfix r) :exec r))
           (x (vex2-byte1-fix x)))
        (part-install r x :width 1 :low 7))
      :exec (the (unsigned-byte 8)
                 (logior (the (unsigned-byte 8)
                              (logand (the (unsigned-byte 8) x)
                                      (the (signed-byte 9) -129)))
                         (the (unsigned-byte 8)
                              (ash (the (unsigned-byte 1) r) 7))))))

Theorem: vex2-byte1-p-of-!vex2-byte1->r

(defthm vex2-byte1-p-of-!vex2-byte1->r
  (b* ((new-x (!vex2-byte1->r$inline r x)))
    (vex2-byte1-p new-x))
  :rule-classes :rewrite)

Theorem: !vex2-byte1->r$inline-of-bfix-r

(defthm !vex2-byte1->r$inline-of-bfix-r
  (equal (!vex2-byte1->r$inline (bfix r) x)
         (!vex2-byte1->r$inline r x)))

Theorem: !vex2-byte1->r$inline-bit-equiv-congruence-on-r

(defthm !vex2-byte1->r$inline-bit-equiv-congruence-on-r
  (implies (bit-equiv r r-equiv)
           (equal (!vex2-byte1->r$inline r x)
                  (!vex2-byte1->r$inline r-equiv x)))
  :rule-classes :congruence)

Theorem: !vex2-byte1->r$inline-of-vex2-byte1-fix-x

(defthm !vex2-byte1->r$inline-of-vex2-byte1-fix-x
  (equal (!vex2-byte1->r$inline r (vex2-byte1-fix x))
         (!vex2-byte1->r$inline r x)))

Theorem: !vex2-byte1->r$inline-vex2-byte1-equiv-congruence-on-x

(defthm !vex2-byte1->r$inline-vex2-byte1-equiv-congruence-on-x
  (implies (vex2-byte1-equiv x x-equiv)
           (equal (!vex2-byte1->r$inline r x)
                  (!vex2-byte1->r$inline r x-equiv)))
  :rule-classes :congruence)

Theorem: !vex2-byte1->r-is-vex2-byte1

(defthm !vex2-byte1->r-is-vex2-byte1
  (equal (!vex2-byte1->r r x)
         (change-vex2-byte1 x :r r)))

Theorem: vex2-byte1->r-of-!vex2-byte1->r

(defthm vex2-byte1->r-of-!vex2-byte1->r
  (b* ((?new-x (!vex2-byte1->r$inline r x)))
    (equal (vex2-byte1->r new-x) (bfix r))))

Theorem: !vex2-byte1->r-equiv-under-mask

(defthm !vex2-byte1->r-equiv-under-mask
  (b* ((?new-x (!vex2-byte1->r$inline r x)))
    (vex2-byte1-equiv-under-mask new-x x 127)))

Function: vex2-byte1-debug$inline

(defun vex2-byte1-debug$inline (x)
  (declare (xargs :guard (vex2-byte1-p x)))
  (b* (((vex2-byte1 x)))
    (cons (cons 'pp x.pp)
          (cons (cons 'l x.l)
                (cons (cons 'vvvv x.vvvv)
                      (cons (cons 'r x.r) nil))))))

Function: vex3-byte1-p$inline

(defun vex3-byte1-p$inline (vex3byte1)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p 8 vex3byte1)
       :exec (and (natp vex3byte1)
                  (< vex3byte1 256))))

Theorem: vex3-byte1-p-when-unsigned-byte-p

(defthm vex3-byte1-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 8 vex3byte1)
           (vex3-byte1-p vex3byte1)))

Theorem: unsigned-byte-p-when-vex3-byte1-p

(defthm unsigned-byte-p-when-vex3-byte1-p
  (implies (vex3-byte1-p vex3byte1)
           (unsigned-byte-p 8 vex3byte1)))

Theorem: vex3-byte1-p-compound-recognizer

(defthm vex3-byte1-p-compound-recognizer
  (implies (vex3-byte1-p vex3byte1)
           (natp vex3byte1))
  :rule-classes :compound-recognizer)

Function: vex3-byte1-fix$inline

(defun vex3-byte1-fix$inline (vex3byte1)
  (declare (xargs :guard (vex3-byte1-p vex3byte1)))
  (mbe :logic (loghead 8 vex3byte1)
       :exec vex3byte1))

Theorem: vex3-byte1-p-of-vex3-byte1-fix

(defthm vex3-byte1-p-of-vex3-byte1-fix
  (b* ((fty::fixed (vex3-byte1-fix$inline vex3byte1)))
    (vex3-byte1-p fty::fixed))
  :rule-classes :rewrite)

Theorem: vex3-byte1-fix-when-vex3-byte1-p

(defthm vex3-byte1-fix-when-vex3-byte1-p
  (implies (vex3-byte1-p vex3byte1)
           (equal (vex3-byte1-fix vex3byte1)
                  vex3byte1)))

Function: vex3-byte1-equiv$inline

(defun vex3-byte1-equiv$inline (x y)
  (declare (xargs :guard (and (vex3-byte1-p x)
                              (vex3-byte1-p y))))
  (equal (vex3-byte1-fix x)
         (vex3-byte1-fix y)))

Theorem: vex3-byte1-equiv-is-an-equivalence

(defthm vex3-byte1-equiv-is-an-equivalence
  (and (booleanp (vex3-byte1-equiv x y))
       (vex3-byte1-equiv x x)
       (implies (vex3-byte1-equiv x y)
                (vex3-byte1-equiv y x))
       (implies (and (vex3-byte1-equiv x y)
                     (vex3-byte1-equiv y z))
                (vex3-byte1-equiv x z)))
  :rule-classes (:equivalence))

Theorem: vex3-byte1-equiv-implies-equal-vex3-byte1-fix-1

(defthm vex3-byte1-equiv-implies-equal-vex3-byte1-fix-1
  (implies (vex3-byte1-equiv x x-equiv)
           (equal (vex3-byte1-fix x)
                  (vex3-byte1-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vex3-byte1-fix-under-vex3-byte1-equiv

(defthm vex3-byte1-fix-under-vex3-byte1-equiv
  (vex3-byte1-equiv (vex3-byte1-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Function: vex3-byte1$inline

(defun vex3-byte1$inline (m-mmmm b x r)
  (declare (xargs :guard (and (5bits-p m-mmmm)
                              (bitp b)
                              (bitp x)
                              (bitp r))))
  (b* ((m-mmmm (mbe :logic (5bits-fix m-mmmm)
                    :exec m-mmmm))
       (b (mbe :logic (bfix b) :exec b))
       (x (mbe :logic (bfix x) :exec x))
       (r (mbe :logic (bfix r) :exec r)))
    (logapp 5 m-mmmm (logapp 1 b (logapp 1 x r)))))

Theorem: vex3-byte1-p-of-vex3-byte1

(defthm vex3-byte1-p-of-vex3-byte1
  (b* ((vex3-byte1 (vex3-byte1$inline m-mmmm b x r)))
    (vex3-byte1-p vex3-byte1))
  :rule-classes :rewrite)

Theorem: vex3-byte1$inline-of-5bits-fix-m-mmmm

(defthm vex3-byte1$inline-of-5bits-fix-m-mmmm
  (equal (vex3-byte1$inline (5bits-fix m-mmmm)
                            b x r)
         (vex3-byte1$inline m-mmmm b x r)))

Theorem: vex3-byte1$inline-5bits-equiv-congruence-on-m-mmmm

(defthm vex3-byte1$inline-5bits-equiv-congruence-on-m-mmmm
  (implies (5bits-equiv m-mmmm m-mmmm-equiv)
           (equal (vex3-byte1$inline m-mmmm b x r)
                  (vex3-byte1$inline m-mmmm-equiv b x r)))
  :rule-classes :congruence)

Theorem: vex3-byte1$inline-of-bfix-b

(defthm vex3-byte1$inline-of-bfix-b
  (equal (vex3-byte1$inline m-mmmm (bfix b) x r)
         (vex3-byte1$inline m-mmmm b x r)))

Theorem: vex3-byte1$inline-bit-equiv-congruence-on-b

(defthm vex3-byte1$inline-bit-equiv-congruence-on-b
  (implies (bit-equiv b b-equiv)
           (equal (vex3-byte1$inline m-mmmm b x r)
                  (vex3-byte1$inline m-mmmm b-equiv x r)))
  :rule-classes :congruence)

Theorem: vex3-byte1$inline-of-bfix-x

(defthm vex3-byte1$inline-of-bfix-x
  (equal (vex3-byte1$inline m-mmmm b (bfix x) r)
         (vex3-byte1$inline m-mmmm b x r)))

Theorem: vex3-byte1$inline-bit-equiv-congruence-on-x

(defthm vex3-byte1$inline-bit-equiv-congruence-on-x
  (implies (bit-equiv x x-equiv)
           (equal (vex3-byte1$inline m-mmmm b x r)
                  (vex3-byte1$inline m-mmmm b x-equiv r)))
  :rule-classes :congruence)

Theorem: vex3-byte1$inline-of-bfix-r

(defthm vex3-byte1$inline-of-bfix-r
  (equal (vex3-byte1$inline m-mmmm b x (bfix r))
         (vex3-byte1$inline m-mmmm b x r)))

Theorem: vex3-byte1$inline-bit-equiv-congruence-on-r

(defthm vex3-byte1$inline-bit-equiv-congruence-on-r
  (implies (bit-equiv r r-equiv)
           (equal (vex3-byte1$inline m-mmmm b x r)
                  (vex3-byte1$inline m-mmmm b x r-equiv)))
  :rule-classes :congruence)

Function: vex3-byte1-equiv-under-mask$inline

(defun vex3-byte1-equiv-under-mask$inline
       (vex3byte1 vex3byte11 mask)
  (declare (xargs :guard (and (vex3-byte1-p vex3byte1)
                              (vex3-byte1-p vex3byte11)
                              (integerp mask))))
  (fty::int-equiv-under-mask (vex3-byte1-fix vex3byte1)
                             (vex3-byte1-fix vex3byte11)
                             mask))

Function: vex3-byte1->m-mmmm$inline

(defun vex3-byte1->m-mmmm$inline (vex3byte1)
  (declare (xargs :guard (vex3-byte1-p vex3byte1)))
  (mbe :logic
       (let ((vex3byte1 (vex3-byte1-fix vex3byte1)))
         (part-select vex3byte1 :low 0 :width 5))
       :exec (the (unsigned-byte 5)
                  (logand (the (unsigned-byte 5) 31)
                          (the (unsigned-byte 8) vex3byte1)))))

Theorem: 5bits-p-of-vex3-byte1->m-mmmm

(defthm 5bits-p-of-vex3-byte1->m-mmmm
  (b* ((m-mmmm (vex3-byte1->m-mmmm$inline vex3byte1)))
    (5bits-p m-mmmm))
  :rule-classes :rewrite)

Theorem: vex3-byte1->m-mmmm$inline-of-vex3-byte1-fix-vex3byte1

(defthm vex3-byte1->m-mmmm$inline-of-vex3-byte1-fix-vex3byte1
  (equal (vex3-byte1->m-mmmm$inline (vex3-byte1-fix vex3byte1))
         (vex3-byte1->m-mmmm$inline vex3byte1)))

Theorem: vex3-byte1->m-mmmm$inline-vex3-byte1-equiv-congruence-on-vex3byte1

(defthm
 vex3-byte1->m-mmmm$inline-vex3-byte1-equiv-congruence-on-vex3byte1
 (implies (vex3-byte1-equiv vex3byte1 vex3byte1-equiv)
          (equal (vex3-byte1->m-mmmm$inline vex3byte1)
                 (vex3-byte1->m-mmmm$inline vex3byte1-equiv)))
 :rule-classes :congruence)

Theorem: vex3-byte1->m-mmmm-of-vex3-byte1

(defthm vex3-byte1->m-mmmm-of-vex3-byte1
  (equal (vex3-byte1->m-mmmm (vex3-byte1 m-mmmm b x r))
         (5bits-fix m-mmmm)))

Theorem: vex3-byte1->m-mmmm-of-write-with-mask

(defthm vex3-byte1->m-mmmm-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     vex3byte1 vex3-byte1-equiv-under-mask)
                (vex3-byte1-equiv-under-mask vex3byte1 y fty::mask)
                (equal (logand (lognot fty::mask) 31)
                       0))
           (equal (vex3-byte1->m-mmmm vex3byte1)
                  (vex3-byte1->m-mmmm y))))

Function: vex3-byte1->b$inline

(defun vex3-byte1->b$inline (vex3byte1)
 (declare (xargs :guard (vex3-byte1-p vex3byte1)))
 (mbe :logic
      (let ((vex3byte1 (vex3-byte1-fix vex3byte1)))
        (part-select vex3byte1 :low 5 :width 1))
      :exec (the (unsigned-byte 1)
                 (logand (the (unsigned-byte 1) 1)
                         (the (unsigned-byte 3)
                              (ash (the (unsigned-byte 8) vex3byte1)
                                   -5))))))

Theorem: bitp-of-vex3-byte1->b

(defthm bitp-of-vex3-byte1->b
  (b* ((b (vex3-byte1->b$inline vex3byte1)))
    (bitp b))
  :rule-classes :rewrite)

Theorem: vex3-byte1->b$inline-of-vex3-byte1-fix-vex3byte1

(defthm vex3-byte1->b$inline-of-vex3-byte1-fix-vex3byte1
  (equal (vex3-byte1->b$inline (vex3-byte1-fix vex3byte1))
         (vex3-byte1->b$inline vex3byte1)))

Theorem: vex3-byte1->b$inline-vex3-byte1-equiv-congruence-on-vex3byte1

(defthm
      vex3-byte1->b$inline-vex3-byte1-equiv-congruence-on-vex3byte1
  (implies (vex3-byte1-equiv vex3byte1 vex3byte1-equiv)
           (equal (vex3-byte1->b$inline vex3byte1)
                  (vex3-byte1->b$inline vex3byte1-equiv)))
  :rule-classes :congruence)

Theorem: vex3-byte1->b-of-vex3-byte1

(defthm vex3-byte1->b-of-vex3-byte1
  (equal (vex3-byte1->b (vex3-byte1 m-mmmm b x r))
         (bfix b)))

Theorem: vex3-byte1->b-of-write-with-mask

(defthm vex3-byte1->b-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     vex3byte1 vex3-byte1-equiv-under-mask)
                (vex3-byte1-equiv-under-mask vex3byte1 y fty::mask)
                (equal (logand (lognot fty::mask) 32)
                       0))
           (equal (vex3-byte1->b vex3byte1)
                  (vex3-byte1->b y))))

Function: vex3-byte1->x$inline

(defun vex3-byte1->x$inline (vex3byte1)
 (declare (xargs :guard (vex3-byte1-p vex3byte1)))
 (mbe :logic
      (let ((vex3byte1 (vex3-byte1-fix vex3byte1)))
        (part-select vex3byte1 :low 6 :width 1))
      :exec (the (unsigned-byte 1)
                 (logand (the (unsigned-byte 1) 1)
                         (the (unsigned-byte 2)
                              (ash (the (unsigned-byte 8) vex3byte1)
                                   -6))))))

Theorem: bitp-of-vex3-byte1->x

(defthm bitp-of-vex3-byte1->x
  (b* ((x (vex3-byte1->x$inline vex3byte1)))
    (bitp x))
  :rule-classes :rewrite)

Theorem: vex3-byte1->x$inline-of-vex3-byte1-fix-vex3byte1

(defthm vex3-byte1->x$inline-of-vex3-byte1-fix-vex3byte1
  (equal (vex3-byte1->x$inline (vex3-byte1-fix vex3byte1))
         (vex3-byte1->x$inline vex3byte1)))

Theorem: vex3-byte1->x$inline-vex3-byte1-equiv-congruence-on-vex3byte1

(defthm
      vex3-byte1->x$inline-vex3-byte1-equiv-congruence-on-vex3byte1
  (implies (vex3-byte1-equiv vex3byte1 vex3byte1-equiv)
           (equal (vex3-byte1->x$inline vex3byte1)
                  (vex3-byte1->x$inline vex3byte1-equiv)))
  :rule-classes :congruence)

Theorem: vex3-byte1->x-of-vex3-byte1

(defthm vex3-byte1->x-of-vex3-byte1
  (equal (vex3-byte1->x (vex3-byte1 m-mmmm b x r))
         (bfix x)))

Theorem: vex3-byte1->x-of-write-with-mask

(defthm vex3-byte1->x-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     vex3byte1 vex3-byte1-equiv-under-mask)
                (vex3-byte1-equiv-under-mask vex3byte1 y fty::mask)
                (equal (logand (lognot fty::mask) 64)
                       0))
           (equal (vex3-byte1->x vex3byte1)
                  (vex3-byte1->x y))))

Function: vex3-byte1->r$inline

(defun vex3-byte1->r$inline (vex3byte1)
 (declare (xargs :guard (vex3-byte1-p vex3byte1)))
 (mbe :logic
      (let ((vex3byte1 (vex3-byte1-fix vex3byte1)))
        (part-select vex3byte1 :low 7 :width 1))
      :exec (the (unsigned-byte 1)
                 (logand (the (unsigned-byte 1) 1)
                         (the (unsigned-byte 1)
                              (ash (the (unsigned-byte 8) vex3byte1)
                                   -7))))))

Theorem: bitp-of-vex3-byte1->r

(defthm bitp-of-vex3-byte1->r
  (b* ((r (vex3-byte1->r$inline vex3byte1)))
    (bitp r))
  :rule-classes :rewrite)

Theorem: vex3-byte1->r$inline-of-vex3-byte1-fix-vex3byte1

(defthm vex3-byte1->r$inline-of-vex3-byte1-fix-vex3byte1
  (equal (vex3-byte1->r$inline (vex3-byte1-fix vex3byte1))
         (vex3-byte1->r$inline vex3byte1)))

Theorem: vex3-byte1->r$inline-vex3-byte1-equiv-congruence-on-vex3byte1

(defthm
      vex3-byte1->r$inline-vex3-byte1-equiv-congruence-on-vex3byte1
  (implies (vex3-byte1-equiv vex3byte1 vex3byte1-equiv)
           (equal (vex3-byte1->r$inline vex3byte1)
                  (vex3-byte1->r$inline vex3byte1-equiv)))
  :rule-classes :congruence)

Theorem: vex3-byte1->r-of-vex3-byte1

(defthm vex3-byte1->r-of-vex3-byte1
  (equal (vex3-byte1->r (vex3-byte1 m-mmmm b x r))
         (bfix r)))

Theorem: vex3-byte1->r-of-write-with-mask

(defthm vex3-byte1->r-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     vex3byte1 vex3-byte1-equiv-under-mask)
                (vex3-byte1-equiv-under-mask vex3byte1 y fty::mask)
                (equal (logand (lognot fty::mask) 128)
                       0))
           (equal (vex3-byte1->r vex3byte1)
                  (vex3-byte1->r y))))

Theorem: vex3-byte1-fix-in-terms-of-vex3-byte1

(defthm vex3-byte1-fix-in-terms-of-vex3-byte1
  (equal (vex3-byte1-fix vex3byte1)
         (change-vex3-byte1 vex3byte1)))

Function: !vex3-byte1->m-mmmm$inline

(defun !vex3-byte1->m-mmmm$inline (m-mmmm vex3byte1)
 (declare (xargs :guard (and (5bits-p m-mmmm)
                             (vex3-byte1-p vex3byte1))))
 (mbe
   :logic
   (b* ((m-mmmm (mbe :logic (5bits-fix m-mmmm)
                     :exec m-mmmm))
        (vex3byte1 (vex3-byte1-fix vex3byte1)))
     (part-install m-mmmm vex3byte1
                   :width 5
                   :low 0))
   :exec (the (unsigned-byte 8)
              (logior (the (unsigned-byte 8)
                           (logand (the (unsigned-byte 8) vex3byte1)
                                   (the (signed-byte 6) -32)))
                      (the (unsigned-byte 5) m-mmmm)))))

Theorem: vex3-byte1-p-of-!vex3-byte1->m-mmmm

(defthm vex3-byte1-p-of-!vex3-byte1->m-mmmm
 (b* ((new-vex3byte1 (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)))
   (vex3-byte1-p new-vex3byte1))
 :rule-classes :rewrite)

Theorem: !vex3-byte1->m-mmmm$inline-of-5bits-fix-m-mmmm

(defthm !vex3-byte1->m-mmmm$inline-of-5bits-fix-m-mmmm
  (equal (!vex3-byte1->m-mmmm$inline (5bits-fix m-mmmm)
                                     vex3byte1)
         (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)))

Theorem: !vex3-byte1->m-mmmm$inline-5bits-equiv-congruence-on-m-mmmm

(defthm !vex3-byte1->m-mmmm$inline-5bits-equiv-congruence-on-m-mmmm
  (implies
       (5bits-equiv m-mmmm m-mmmm-equiv)
       (equal (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)
              (!vex3-byte1->m-mmmm$inline m-mmmm-equiv vex3byte1)))
  :rule-classes :congruence)

Theorem: !vex3-byte1->m-mmmm$inline-of-vex3-byte1-fix-vex3byte1

(defthm !vex3-byte1->m-mmmm$inline-of-vex3-byte1-fix-vex3byte1
 (equal
      (!vex3-byte1->m-mmmm$inline m-mmmm (vex3-byte1-fix vex3byte1))
      (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)))

Theorem: !vex3-byte1->m-mmmm$inline-vex3-byte1-equiv-congruence-on-vex3byte1

(defthm
 !vex3-byte1->m-mmmm$inline-vex3-byte1-equiv-congruence-on-vex3byte1
 (implies
      (vex3-byte1-equiv vex3byte1 vex3byte1-equiv)
      (equal (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)
             (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1-equiv)))
 :rule-classes :congruence)

Theorem: !vex3-byte1->m-mmmm-is-vex3-byte1

(defthm !vex3-byte1->m-mmmm-is-vex3-byte1
  (equal (!vex3-byte1->m-mmmm m-mmmm vex3byte1)
         (change-vex3-byte1 vex3byte1
                            :m-mmmm m-mmmm)))

Theorem: vex3-byte1->m-mmmm-of-!vex3-byte1->m-mmmm

(defthm vex3-byte1->m-mmmm-of-!vex3-byte1->m-mmmm
  (b*
    ((?new-vex3byte1 (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)))
    (equal (vex3-byte1->m-mmmm new-vex3byte1)
           (5bits-fix m-mmmm))))

Theorem: !vex3-byte1->m-mmmm-equiv-under-mask

(defthm !vex3-byte1->m-mmmm-equiv-under-mask
  (b*
    ((?new-vex3byte1 (!vex3-byte1->m-mmmm$inline m-mmmm vex3byte1)))
    (vex3-byte1-equiv-under-mask new-vex3byte1 vex3byte1 -32)))

Function: !vex3-byte1->b$inline

(defun !vex3-byte1->b$inline (b vex3byte1)
 (declare (xargs :guard (and (bitp b)
                             (vex3-byte1-p vex3byte1))))
 (mbe
   :logic
   (b* ((b (mbe :logic (bfix b) :exec b))
        (vex3byte1 (vex3-byte1-fix vex3byte1)))
     (part-install b vex3byte1
                   :width 1
                   :low 5))
   :exec (the (unsigned-byte 8)
              (logior (the (unsigned-byte 8)
                           (logand (the (unsigned-byte 8) vex3byte1)
                                   (the (signed-byte 7) -33)))
                      (the (unsigned-byte 6)
                           (ash (the (unsigned-byte 1) b) 5))))))

Theorem: vex3-byte1-p-of-!vex3-byte1->b

(defthm vex3-byte1-p-of-!vex3-byte1->b
  (b* ((new-vex3byte1 (!vex3-byte1->b$inline b vex3byte1)))
    (vex3-byte1-p new-vex3byte1))
  :rule-classes :rewrite)

Theorem: !vex3-byte1->b$inline-of-bfix-b

(defthm !vex3-byte1->b$inline-of-bfix-b
  (equal (!vex3-byte1->b$inline (bfix b)
                                vex3byte1)
         (!vex3-byte1->b$inline b vex3byte1)))

Theorem: !vex3-byte1->b$inline-bit-equiv-congruence-on-b

(defthm !vex3-byte1->b$inline-bit-equiv-congruence-on-b
  (implies (bit-equiv b b-equiv)
           (equal (!vex3-byte1->b$inline b vex3byte1)
                  (!vex3-byte1->b$inline b-equiv vex3byte1)))
  :rule-classes :congruence)

Theorem: !vex3-byte1->b$inline-of-vex3-byte1-fix-vex3byte1

(defthm !vex3-byte1->b$inline-of-vex3-byte1-fix-vex3byte1
  (equal (!vex3-byte1->b$inline b (vex3-byte1-fix vex3byte1))
         (!vex3-byte1->b$inline b vex3byte1)))

Theorem: !vex3-byte1->b$inline-vex3-byte1-equiv-congruence-on-vex3byte1

(defthm
     !vex3-byte1->b$inline-vex3-byte1-equiv-congruence-on-vex3byte1
  (implies (vex3-byte1-equiv vex3byte1 vex3byte1-equiv)
           (equal (!vex3-byte1->b$inline b vex3byte1)
                  (!vex3-byte1->b$inline b vex3byte1-equiv)))
  :rule-classes :congruence)

Theorem: !vex3-byte1->b-is-vex3-byte1

(defthm !vex3-byte1->b-is-vex3-byte1
  (equal (!vex3-byte1->b b vex3byte1)
         (change-vex3-byte1 vex3byte1 :b b)))

Theorem: vex3-byte1->b-of-!vex3-byte1->b

(defthm vex3-byte1->b-of-!vex3-byte1->b
  (b* ((?new-vex3byte1 (!vex3-byte1->b$inline b vex3byte1)))
    (equal (vex3-byte1->b new-vex3byte1)
           (bfix b))))

Theorem: !vex3-byte1->b-equiv-under-mask

(defthm !vex3-byte1->b-equiv-under-mask
  (b* ((?new-vex3byte1 (!vex3-byte1->b$inline b vex3byte1)))
    (vex3-byte1-equiv-under-mask new-vex3byte1 vex3byte1 -33)))

Function: !vex3-byte1->x$inline

(defun !vex3-byte1->x$inline (x vex3byte1)
 (declare (xargs :guard (and (bitp x)
                             (vex3-byte1-p vex3byte1))))
 (mbe
   :logic
   (b* ((x (mbe :logic (bfix x) :exec x))
        (vex3byte1 (vex3-byte1-fix vex3byte1)))
     (part-install x vex3byte1
                   :width 1
                   :low 6))
   :exec (the (unsigned-byte 8)
              (logior (the (unsigned-byte 8)
                           (logand (the (unsigned-byte 8) vex3byte1)
                                   (the (signed-byte 8) -65)))
                      (the (unsigned-byte 7)
                           (ash (the (unsigned-byte 1) x) 6))))))

Theorem: vex3-byte1-p-of-!vex3-byte1->x

(defthm vex3-byte1-p-of-!vex3-byte1->x
  (b* ((new-vex3byte1 (!vex3-byte1->x$inline x vex3byte1)))
    (vex3-byte1-p new-vex3byte1))
  :rule-classes :rewrite)

Theorem: !vex3-byte1->x$inline-of-bfix-x

(defthm !vex3-byte1->x$inline-of-bfix-x
  (equal (!vex3-byte1->x$inline (bfix x)
                                vex3byte1)
         (!vex3-byte1->x$inline x vex3byte1)))

Theorem: !vex3-byte1->x$inline-bit-equiv-congruence-on-x

(defthm !vex3-byte1->x$inline-bit-equiv-congruence-on-x
  (implies (bit-equiv x x-equiv)
           (equal (!vex3-byte1->x$inline x vex3byte1)
                  (!vex3-byte1->x$inline x-equiv vex3byte1)))
  :rule-classes :congruence)

Theorem: !vex3-byte1->x$inline-of-vex3-byte1-fix-vex3byte1

(defthm !vex3-byte1->x$inline-of-vex3-byte1-fix-vex3byte1
  (equal (!vex3-byte1->x$inline x (vex3-byte1-fix vex3byte1))
         (!vex3-byte1->x$inline x vex3byte1)))

Theorem: !vex3-byte1->x$inline-vex3-byte1-equiv-congruence-on-vex3byte1

(defthm
     !vex3-byte1->x$inline-vex3-byte1-equiv-congruence-on-vex3byte1
  (implies (vex3-byte1-equiv vex3byte1 vex3byte1-equiv)
           (equal (!vex3-byte1->x$inline x vex3byte1)
                  (!vex3-byte1->x$inline x vex3byte1-equiv)))
  :rule-classes :congruence)

Theorem: !vex3-byte1->x-is-vex3-byte1

(defthm !vex3-byte1->x-is-vex3-byte1
  (equal (!vex3-byte1->x x vex3byte1)
         (change-vex3-byte1 vex3byte1 :x x)))

Theorem: vex3-byte1->x-of-!vex3-byte1->x

(defthm vex3-byte1->x-of-!vex3-byte1->x
  (b* ((?new-vex3byte1 (!vex3-byte1->x$inline x vex3byte1)))
    (equal (vex3-byte1->x new-vex3byte1)
           (bfix x))))

Theorem: !vex3-byte1->x-equiv-under-mask

(defthm !vex3-byte1->x-equiv-under-mask
  (b* ((?new-vex3byte1 (!vex3-byte1->x$inline x vex3byte1)))
    (vex3-byte1-equiv-under-mask new-vex3byte1 vex3byte1 -65)))

Function: !vex3-byte1->r$inline

(defun !vex3-byte1->r$inline (r vex3byte1)
 (declare (xargs :guard (and (bitp r)
                             (vex3-byte1-p vex3byte1))))
 (mbe
   :logic
   (b* ((r (mbe :logic (bfix r) :exec r))
        (vex3byte1 (vex3-byte1-fix vex3byte1)))
     (part-install r vex3byte1
                   :width 1
                   :low 7))
   :exec (the (unsigned-byte 8)
              (logior (the (unsigned-byte 8)
                           (logand (the (unsigned-byte 8) vex3byte1)
                                   (the (signed-byte 9) -129)))
                      (the (unsigned-byte 8)
                           (ash (the (unsigned-byte 1) r) 7))))))

Theorem: vex3-byte1-p-of-!vex3-byte1->r

(defthm vex3-byte1-p-of-!vex3-byte1->r
  (b* ((new-vex3byte1 (!vex3-byte1->r$inline r vex3byte1)))
    (vex3-byte1-p new-vex3byte1))
  :rule-classes :rewrite)

Theorem: !vex3-byte1->r$inline-of-bfix-r

(defthm !vex3-byte1->r$inline-of-bfix-r
  (equal (!vex3-byte1->r$inline (bfix r)
                                vex3byte1)
         (!vex3-byte1->r$inline r vex3byte1)))

Theorem: !vex3-byte1->r$inline-bit-equiv-congruence-on-r

(defthm !vex3-byte1->r$inline-bit-equiv-congruence-on-r
  (implies (bit-equiv r r-equiv)
           (equal (!vex3-byte1->r$inline r vex3byte1)
                  (!vex3-byte1->r$inline r-equiv vex3byte1)))
  :rule-classes :congruence)

Theorem: !vex3-byte1->r$inline-of-vex3-byte1-fix-vex3byte1

(defthm !vex3-byte1->r$inline-of-vex3-byte1-fix-vex3byte1
  (equal (!vex3-byte1->r$inline r (vex3-byte1-fix vex3byte1))
         (!vex3-byte1->r$inline r vex3byte1)))

Theorem: !vex3-byte1->r$inline-vex3-byte1-equiv-congruence-on-vex3byte1

(defthm
     !vex3-byte1->r$inline-vex3-byte1-equiv-congruence-on-vex3byte1
  (implies (vex3-byte1-equiv vex3byte1 vex3byte1-equiv)
           (equal (!vex3-byte1->r$inline r vex3byte1)
                  (!vex3-byte1->r$inline r vex3byte1-equiv)))
  :rule-classes :congruence)

Theorem: !vex3-byte1->r-is-vex3-byte1

(defthm !vex3-byte1->r-is-vex3-byte1
  (equal (!vex3-byte1->r r vex3byte1)
         (change-vex3-byte1 vex3byte1 :r r)))

Theorem: vex3-byte1->r-of-!vex3-byte1->r

(defthm vex3-byte1->r-of-!vex3-byte1->r
  (b* ((?new-vex3byte1 (!vex3-byte1->r$inline r vex3byte1)))
    (equal (vex3-byte1->r new-vex3byte1)
           (bfix r))))

Theorem: !vex3-byte1->r-equiv-under-mask

(defthm !vex3-byte1->r-equiv-under-mask
  (b* ((?new-vex3byte1 (!vex3-byte1->r$inline r vex3byte1)))
    (vex3-byte1-equiv-under-mask new-vex3byte1 vex3byte1 127)))

Function: vex3-byte1-debug$inline

(defun vex3-byte1-debug$inline (vex3byte1)
  (declare (xargs :guard (vex3-byte1-p vex3byte1)))
  (b* (((vex3-byte1 vex3byte1)))
    (cons (cons 'm-mmmm vex3byte1.m-mmmm)
          (cons (cons 'b vex3byte1.b)
                (cons (cons 'x vex3byte1.x)
                      (cons (cons 'r vex3byte1.r) nil))))))

Function: vex3-byte2-p$inline

(defun vex3-byte2-p$inline (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p 8 x)
       :exec (and (natp x) (< x 256))))

Theorem: vex3-byte2-p-when-unsigned-byte-p

(defthm vex3-byte2-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 8 x)
           (vex3-byte2-p x)))

Theorem: unsigned-byte-p-when-vex3-byte2-p

(defthm unsigned-byte-p-when-vex3-byte2-p
  (implies (vex3-byte2-p x)
           (unsigned-byte-p 8 x)))

Theorem: vex3-byte2-p-compound-recognizer

(defthm vex3-byte2-p-compound-recognizer
  (implies (vex3-byte2-p x) (natp x))
  :rule-classes :compound-recognizer)

Function: vex3-byte2-fix$inline

(defun vex3-byte2-fix$inline (x)
  (declare (xargs :guard (vex3-byte2-p x)))
  (mbe :logic (loghead 8 x) :exec x))

Theorem: vex3-byte2-p-of-vex3-byte2-fix

(defthm vex3-byte2-p-of-vex3-byte2-fix
  (b* ((fty::fixed (vex3-byte2-fix$inline x)))
    (vex3-byte2-p fty::fixed))
  :rule-classes :rewrite)

Theorem: vex3-byte2-fix-when-vex3-byte2-p

(defthm vex3-byte2-fix-when-vex3-byte2-p
  (implies (vex3-byte2-p x)
           (equal (vex3-byte2-fix x) x)))

Function: vex3-byte2-equiv$inline

(defun vex3-byte2-equiv$inline (x y)
  (declare (xargs :guard (and (vex3-byte2-p x)
                              (vex3-byte2-p y))))
  (equal (vex3-byte2-fix x)
         (vex3-byte2-fix y)))

Theorem: vex3-byte2-equiv-is-an-equivalence

(defthm vex3-byte2-equiv-is-an-equivalence
  (and (booleanp (vex3-byte2-equiv x y))
       (vex3-byte2-equiv x x)
       (implies (vex3-byte2-equiv x y)
                (vex3-byte2-equiv y x))
       (implies (and (vex3-byte2-equiv x y)
                     (vex3-byte2-equiv y z))
                (vex3-byte2-equiv x z)))
  :rule-classes (:equivalence))

Theorem: vex3-byte2-equiv-implies-equal-vex3-byte2-fix-1

(defthm vex3-byte2-equiv-implies-equal-vex3-byte2-fix-1
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (vex3-byte2-fix x)
                  (vex3-byte2-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: vex3-byte2-fix-under-vex3-byte2-equiv

(defthm vex3-byte2-fix-under-vex3-byte2-equiv
  (vex3-byte2-equiv (vex3-byte2-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Function: vex3-byte2$inline

(defun vex3-byte2$inline (pp l vvvv w)
  (declare (xargs :guard (and (2bits-p pp)
                              (bitp l)
                              (4bits-p vvvv)
                              (bitp w))))
  (b* ((pp (mbe :logic (2bits-fix pp) :exec pp))
       (l (mbe :logic (bfix l) :exec l))
       (vvvv (mbe :logic (4bits-fix vvvv)
                  :exec vvvv))
       (w (mbe :logic (bfix w) :exec w)))
    (logapp 2 pp (logapp 1 l (logapp 4 vvvv w)))))

Theorem: vex3-byte2-p-of-vex3-byte2

(defthm vex3-byte2-p-of-vex3-byte2
  (b* ((vex3-byte2 (vex3-byte2$inline pp l vvvv w)))
    (vex3-byte2-p vex3-byte2))
  :rule-classes :rewrite)

Theorem: vex3-byte2$inline-of-2bits-fix-pp

(defthm vex3-byte2$inline-of-2bits-fix-pp
  (equal (vex3-byte2$inline (2bits-fix pp)
                            l vvvv w)
         (vex3-byte2$inline pp l vvvv w)))

Theorem: vex3-byte2$inline-2bits-equiv-congruence-on-pp

(defthm vex3-byte2$inline-2bits-equiv-congruence-on-pp
  (implies (2bits-equiv pp pp-equiv)
           (equal (vex3-byte2$inline pp l vvvv w)
                  (vex3-byte2$inline pp-equiv l vvvv w)))
  :rule-classes :congruence)

Theorem: vex3-byte2$inline-of-bfix-l

(defthm vex3-byte2$inline-of-bfix-l
  (equal (vex3-byte2$inline pp (bfix l) vvvv w)
         (vex3-byte2$inline pp l vvvv w)))

Theorem: vex3-byte2$inline-bit-equiv-congruence-on-l

(defthm vex3-byte2$inline-bit-equiv-congruence-on-l
  (implies (bit-equiv l l-equiv)
           (equal (vex3-byte2$inline pp l vvvv w)
                  (vex3-byte2$inline pp l-equiv vvvv w)))
  :rule-classes :congruence)

Theorem: vex3-byte2$inline-of-4bits-fix-vvvv

(defthm vex3-byte2$inline-of-4bits-fix-vvvv
  (equal (vex3-byte2$inline pp l (4bits-fix vvvv)
                            w)
         (vex3-byte2$inline pp l vvvv w)))

Theorem: vex3-byte2$inline-4bits-equiv-congruence-on-vvvv

(defthm vex3-byte2$inline-4bits-equiv-congruence-on-vvvv
  (implies (4bits-equiv vvvv vvvv-equiv)
           (equal (vex3-byte2$inline pp l vvvv w)
                  (vex3-byte2$inline pp l vvvv-equiv w)))
  :rule-classes :congruence)

Theorem: vex3-byte2$inline-of-bfix-w

(defthm vex3-byte2$inline-of-bfix-w
  (equal (vex3-byte2$inline pp l vvvv (bfix w))
         (vex3-byte2$inline pp l vvvv w)))

Theorem: vex3-byte2$inline-bit-equiv-congruence-on-w

(defthm vex3-byte2$inline-bit-equiv-congruence-on-w
  (implies (bit-equiv w w-equiv)
           (equal (vex3-byte2$inline pp l vvvv w)
                  (vex3-byte2$inline pp l vvvv w-equiv)))
  :rule-classes :congruence)

Function: vex3-byte2-equiv-under-mask$inline

(defun vex3-byte2-equiv-under-mask$inline (x x1 mask)
  (declare (xargs :guard (and (vex3-byte2-p x)
                              (vex3-byte2-p x1)
                              (integerp mask))))
  (fty::int-equiv-under-mask (vex3-byte2-fix x)
                             (vex3-byte2-fix x1)
                             mask))

Function: vex3-byte2->pp$inline

(defun vex3-byte2->pp$inline (x)
  (declare (xargs :guard (vex3-byte2-p x)))
  (mbe :logic
       (let ((x (vex3-byte2-fix x)))
         (part-select x :low 0 :width 2))
       :exec (the (unsigned-byte 2)
                  (logand (the (unsigned-byte 2) 3)
                          (the (unsigned-byte 8) x)))))

Theorem: 2bits-p-of-vex3-byte2->pp

(defthm 2bits-p-of-vex3-byte2->pp
  (b* ((pp (vex3-byte2->pp$inline x)))
    (2bits-p pp))
  :rule-classes :rewrite)

Theorem: vex3-byte2->pp$inline-of-vex3-byte2-fix-x

(defthm vex3-byte2->pp$inline-of-vex3-byte2-fix-x
  (equal (vex3-byte2->pp$inline (vex3-byte2-fix x))
         (vex3-byte2->pp$inline x)))

Theorem: vex3-byte2->pp$inline-vex3-byte2-equiv-congruence-on-x

(defthm vex3-byte2->pp$inline-vex3-byte2-equiv-congruence-on-x
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (vex3-byte2->pp$inline x)
                  (vex3-byte2->pp$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex3-byte2->pp-of-vex3-byte2

(defthm vex3-byte2->pp-of-vex3-byte2
  (equal (vex3-byte2->pp (vex3-byte2 pp l vvvv w))
         (2bits-fix pp)))

Theorem: vex3-byte2->pp-of-write-with-mask

(defthm vex3-byte2->pp-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex3-byte2-equiv-under-mask)
                (vex3-byte2-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 3) 0))
           (equal (vex3-byte2->pp x)
                  (vex3-byte2->pp y))))

Function: vex3-byte2->l$inline

(defun vex3-byte2->l$inline (x)
 (declare (xargs :guard (vex3-byte2-p x)))
 (mbe
     :logic
     (let ((x (vex3-byte2-fix x)))
       (part-select x :low 2 :width 1))
     :exec (the (unsigned-byte 1)
                (logand (the (unsigned-byte 1) 1)
                        (the (unsigned-byte 6)
                             (ash (the (unsigned-byte 8) x) -2))))))

Theorem: bitp-of-vex3-byte2->l

(defthm bitp-of-vex3-byte2->l
  (b* ((l (vex3-byte2->l$inline x)))
    (bitp l))
  :rule-classes :rewrite)

Theorem: vex3-byte2->l$inline-of-vex3-byte2-fix-x

(defthm vex3-byte2->l$inline-of-vex3-byte2-fix-x
  (equal (vex3-byte2->l$inline (vex3-byte2-fix x))
         (vex3-byte2->l$inline x)))

Theorem: vex3-byte2->l$inline-vex3-byte2-equiv-congruence-on-x

(defthm vex3-byte2->l$inline-vex3-byte2-equiv-congruence-on-x
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (vex3-byte2->l$inline x)
                  (vex3-byte2->l$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex3-byte2->l-of-vex3-byte2

(defthm vex3-byte2->l-of-vex3-byte2
  (equal (vex3-byte2->l (vex3-byte2 pp l vvvv w))
         (bfix l)))

Theorem: vex3-byte2->l-of-write-with-mask

(defthm vex3-byte2->l-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex3-byte2-equiv-under-mask)
                (vex3-byte2-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 4) 0))
           (equal (vex3-byte2->l x)
                  (vex3-byte2->l y))))

Function: vex3-byte2->vvvv$inline

(defun vex3-byte2->vvvv$inline (x)
 (declare (xargs :guard (vex3-byte2-p x)))
 (mbe
     :logic
     (let ((x (vex3-byte2-fix x)))
       (part-select x :low 3 :width 4))
     :exec (the (unsigned-byte 4)
                (logand (the (unsigned-byte 4) 15)
                        (the (unsigned-byte 5)
                             (ash (the (unsigned-byte 8) x) -3))))))

Theorem: 4bits-p-of-vex3-byte2->vvvv

(defthm 4bits-p-of-vex3-byte2->vvvv
  (b* ((vvvv (vex3-byte2->vvvv$inline x)))
    (4bits-p vvvv))
  :rule-classes :rewrite)

Theorem: vex3-byte2->vvvv$inline-of-vex3-byte2-fix-x

(defthm vex3-byte2->vvvv$inline-of-vex3-byte2-fix-x
  (equal (vex3-byte2->vvvv$inline (vex3-byte2-fix x))
         (vex3-byte2->vvvv$inline x)))

Theorem: vex3-byte2->vvvv$inline-vex3-byte2-equiv-congruence-on-x

(defthm vex3-byte2->vvvv$inline-vex3-byte2-equiv-congruence-on-x
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (vex3-byte2->vvvv$inline x)
                  (vex3-byte2->vvvv$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex3-byte2->vvvv-of-vex3-byte2

(defthm vex3-byte2->vvvv-of-vex3-byte2
  (equal (vex3-byte2->vvvv (vex3-byte2 pp l vvvv w))
         (4bits-fix vvvv)))

Theorem: vex3-byte2->vvvv-of-write-with-mask

(defthm vex3-byte2->vvvv-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex3-byte2-equiv-under-mask)
                (vex3-byte2-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 120)
                       0))
           (equal (vex3-byte2->vvvv x)
                  (vex3-byte2->vvvv y))))

Function: vex3-byte2->w$inline

(defun vex3-byte2->w$inline (x)
 (declare (xargs :guard (vex3-byte2-p x)))
 (mbe
     :logic
     (let ((x (vex3-byte2-fix x)))
       (part-select x :low 7 :width 1))
     :exec (the (unsigned-byte 1)
                (logand (the (unsigned-byte 1) 1)
                        (the (unsigned-byte 1)
                             (ash (the (unsigned-byte 8) x) -7))))))

Theorem: bitp-of-vex3-byte2->w

(defthm bitp-of-vex3-byte2->w
  (b* ((w (vex3-byte2->w$inline x)))
    (bitp w))
  :rule-classes :rewrite)

Theorem: vex3-byte2->w$inline-of-vex3-byte2-fix-x

(defthm vex3-byte2->w$inline-of-vex3-byte2-fix-x
  (equal (vex3-byte2->w$inline (vex3-byte2-fix x))
         (vex3-byte2->w$inline x)))

Theorem: vex3-byte2->w$inline-vex3-byte2-equiv-congruence-on-x

(defthm vex3-byte2->w$inline-vex3-byte2-equiv-congruence-on-x
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (vex3-byte2->w$inline x)
                  (vex3-byte2->w$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex3-byte2->w-of-vex3-byte2

(defthm vex3-byte2->w-of-vex3-byte2
  (equal (vex3-byte2->w (vex3-byte2 pp l vvvv w))
         (bfix w)))

Theorem: vex3-byte2->w-of-write-with-mask

(defthm vex3-byte2->w-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex3-byte2-equiv-under-mask)
                (vex3-byte2-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 128)
                       0))
           (equal (vex3-byte2->w x)
                  (vex3-byte2->w y))))

Theorem: vex3-byte2-fix-in-terms-of-vex3-byte2

(defthm vex3-byte2-fix-in-terms-of-vex3-byte2
  (equal (vex3-byte2-fix x)
         (change-vex3-byte2 x)))

Function: !vex3-byte2->pp$inline

(defun !vex3-byte2->pp$inline (pp x)
  (declare (xargs :guard (and (2bits-p pp) (vex3-byte2-p x))))
  (mbe :logic
       (b* ((pp (mbe :logic (2bits-fix pp) :exec pp))
            (x (vex3-byte2-fix x)))
         (part-install pp x :width 2 :low 0))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 3) -4)))
                          (the (unsigned-byte 2) pp)))))

Theorem: vex3-byte2-p-of-!vex3-byte2->pp

(defthm vex3-byte2-p-of-!vex3-byte2->pp
  (b* ((new-x (!vex3-byte2->pp$inline pp x)))
    (vex3-byte2-p new-x))
  :rule-classes :rewrite)

Theorem: !vex3-byte2->pp$inline-of-2bits-fix-pp

(defthm !vex3-byte2->pp$inline-of-2bits-fix-pp
  (equal (!vex3-byte2->pp$inline (2bits-fix pp)
                                 x)
         (!vex3-byte2->pp$inline pp x)))

Theorem: !vex3-byte2->pp$inline-2bits-equiv-congruence-on-pp

(defthm !vex3-byte2->pp$inline-2bits-equiv-congruence-on-pp
  (implies (2bits-equiv pp pp-equiv)
           (equal (!vex3-byte2->pp$inline pp x)
                  (!vex3-byte2->pp$inline pp-equiv x)))
  :rule-classes :congruence)

Theorem: !vex3-byte2->pp$inline-of-vex3-byte2-fix-x

(defthm !vex3-byte2->pp$inline-of-vex3-byte2-fix-x
  (equal (!vex3-byte2->pp$inline pp (vex3-byte2-fix x))
         (!vex3-byte2->pp$inline pp x)))

Theorem: !vex3-byte2->pp$inline-vex3-byte2-equiv-congruence-on-x

(defthm !vex3-byte2->pp$inline-vex3-byte2-equiv-congruence-on-x
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (!vex3-byte2->pp$inline pp x)
                  (!vex3-byte2->pp$inline pp x-equiv)))
  :rule-classes :congruence)

Theorem: !vex3-byte2->pp-is-vex3-byte2

(defthm !vex3-byte2->pp-is-vex3-byte2
  (equal (!vex3-byte2->pp pp x)
         (change-vex3-byte2 x :pp pp)))

Theorem: vex3-byte2->pp-of-!vex3-byte2->pp

(defthm vex3-byte2->pp-of-!vex3-byte2->pp
  (b* ((?new-x (!vex3-byte2->pp$inline pp x)))
    (equal (vex3-byte2->pp new-x)
           (2bits-fix pp))))

Theorem: !vex3-byte2->pp-equiv-under-mask

(defthm !vex3-byte2->pp-equiv-under-mask
  (b* ((?new-x (!vex3-byte2->pp$inline pp x)))
    (vex3-byte2-equiv-under-mask new-x x -4)))

Function: !vex3-byte2->l$inline

(defun !vex3-byte2->l$inline (l x)
 (declare (xargs :guard (and (bitp l) (vex3-byte2-p x))))
 (mbe :logic
      (b* ((l (mbe :logic (bfix l) :exec l))
           (x (vex3-byte2-fix x)))
        (part-install l x :width 1 :low 2))
      :exec (the (unsigned-byte 8)
                 (logior (the (unsigned-byte 8)
                              (logand (the (unsigned-byte 8) x)
                                      (the (signed-byte 4) -5)))
                         (the (unsigned-byte 3)
                              (ash (the (unsigned-byte 1) l) 2))))))

Theorem: vex3-byte2-p-of-!vex3-byte2->l

(defthm vex3-byte2-p-of-!vex3-byte2->l
  (b* ((new-x (!vex3-byte2->l$inline l x)))
    (vex3-byte2-p new-x))
  :rule-classes :rewrite)

Theorem: !vex3-byte2->l$inline-of-bfix-l

(defthm !vex3-byte2->l$inline-of-bfix-l
  (equal (!vex3-byte2->l$inline (bfix l) x)
         (!vex3-byte2->l$inline l x)))

Theorem: !vex3-byte2->l$inline-bit-equiv-congruence-on-l

(defthm !vex3-byte2->l$inline-bit-equiv-congruence-on-l
  (implies (bit-equiv l l-equiv)
           (equal (!vex3-byte2->l$inline l x)
                  (!vex3-byte2->l$inline l-equiv x)))
  :rule-classes :congruence)

Theorem: !vex3-byte2->l$inline-of-vex3-byte2-fix-x

(defthm !vex3-byte2->l$inline-of-vex3-byte2-fix-x
  (equal (!vex3-byte2->l$inline l (vex3-byte2-fix x))
         (!vex3-byte2->l$inline l x)))

Theorem: !vex3-byte2->l$inline-vex3-byte2-equiv-congruence-on-x

(defthm !vex3-byte2->l$inline-vex3-byte2-equiv-congruence-on-x
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (!vex3-byte2->l$inline l x)
                  (!vex3-byte2->l$inline l x-equiv)))
  :rule-classes :congruence)

Theorem: !vex3-byte2->l-is-vex3-byte2

(defthm !vex3-byte2->l-is-vex3-byte2
  (equal (!vex3-byte2->l l x)
         (change-vex3-byte2 x :l l)))

Theorem: vex3-byte2->l-of-!vex3-byte2->l

(defthm vex3-byte2->l-of-!vex3-byte2->l
  (b* ((?new-x (!vex3-byte2->l$inline l x)))
    (equal (vex3-byte2->l new-x) (bfix l))))

Theorem: !vex3-byte2->l-equiv-under-mask

(defthm !vex3-byte2->l-equiv-under-mask
  (b* ((?new-x (!vex3-byte2->l$inline l x)))
    (vex3-byte2-equiv-under-mask new-x x -5)))

Function: !vex3-byte2->vvvv$inline

(defun !vex3-byte2->vvvv$inline (vvvv x)
  (declare (xargs :guard (and (4bits-p vvvv) (vex3-byte2-p x))))
  (mbe :logic
       (b* ((vvvv (mbe :logic (4bits-fix vvvv)
                       :exec vvvv))
            (x (vex3-byte2-fix x)))
         (part-install vvvv x :width 4 :low 3))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 8) -121)))
                          (the (unsigned-byte 7)
                               (ash (the (unsigned-byte 4) vvvv)
                                    3))))))

Theorem: vex3-byte2-p-of-!vex3-byte2->vvvv

(defthm vex3-byte2-p-of-!vex3-byte2->vvvv
  (b* ((new-x (!vex3-byte2->vvvv$inline vvvv x)))
    (vex3-byte2-p new-x))
  :rule-classes :rewrite)

Theorem: !vex3-byte2->vvvv$inline-of-4bits-fix-vvvv

(defthm !vex3-byte2->vvvv$inline-of-4bits-fix-vvvv
  (equal (!vex3-byte2->vvvv$inline (4bits-fix vvvv)
                                   x)
         (!vex3-byte2->vvvv$inline vvvv x)))

Theorem: !vex3-byte2->vvvv$inline-4bits-equiv-congruence-on-vvvv

(defthm !vex3-byte2->vvvv$inline-4bits-equiv-congruence-on-vvvv
  (implies (4bits-equiv vvvv vvvv-equiv)
           (equal (!vex3-byte2->vvvv$inline vvvv x)
                  (!vex3-byte2->vvvv$inline vvvv-equiv x)))
  :rule-classes :congruence)

Theorem: !vex3-byte2->vvvv$inline-of-vex3-byte2-fix-x

(defthm !vex3-byte2->vvvv$inline-of-vex3-byte2-fix-x
  (equal (!vex3-byte2->vvvv$inline vvvv (vex3-byte2-fix x))
         (!vex3-byte2->vvvv$inline vvvv x)))

Theorem: !vex3-byte2->vvvv$inline-vex3-byte2-equiv-congruence-on-x

(defthm !vex3-byte2->vvvv$inline-vex3-byte2-equiv-congruence-on-x
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (!vex3-byte2->vvvv$inline vvvv x)
                  (!vex3-byte2->vvvv$inline vvvv x-equiv)))
  :rule-classes :congruence)

Theorem: !vex3-byte2->vvvv-is-vex3-byte2

(defthm !vex3-byte2->vvvv-is-vex3-byte2
  (equal (!vex3-byte2->vvvv vvvv x)
         (change-vex3-byte2 x :vvvv vvvv)))

Theorem: vex3-byte2->vvvv-of-!vex3-byte2->vvvv

(defthm vex3-byte2->vvvv-of-!vex3-byte2->vvvv
  (b* ((?new-x (!vex3-byte2->vvvv$inline vvvv x)))
    (equal (vex3-byte2->vvvv new-x)
           (4bits-fix vvvv))))

Theorem: !vex3-byte2->vvvv-equiv-under-mask

(defthm !vex3-byte2->vvvv-equiv-under-mask
  (b* ((?new-x (!vex3-byte2->vvvv$inline vvvv x)))
    (vex3-byte2-equiv-under-mask new-x x -121)))

Function: !vex3-byte2->w$inline

(defun !vex3-byte2->w$inline (w x)
 (declare (xargs :guard (and (bitp w) (vex3-byte2-p x))))
 (mbe :logic
      (b* ((w (mbe :logic (bfix w) :exec w))
           (x (vex3-byte2-fix x)))
        (part-install w x :width 1 :low 7))
      :exec (the (unsigned-byte 8)
                 (logior (the (unsigned-byte 8)
                              (logand (the (unsigned-byte 8) x)
                                      (the (signed-byte 9) -129)))
                         (the (unsigned-byte 8)
                              (ash (the (unsigned-byte 1) w) 7))))))

Theorem: vex3-byte2-p-of-!vex3-byte2->w

(defthm vex3-byte2-p-of-!vex3-byte2->w
  (b* ((new-x (!vex3-byte2->w$inline w x)))
    (vex3-byte2-p new-x))
  :rule-classes :rewrite)

Theorem: !vex3-byte2->w$inline-of-bfix-w

(defthm !vex3-byte2->w$inline-of-bfix-w
  (equal (!vex3-byte2->w$inline (bfix w) x)
         (!vex3-byte2->w$inline w x)))

Theorem: !vex3-byte2->w$inline-bit-equiv-congruence-on-w

(defthm !vex3-byte2->w$inline-bit-equiv-congruence-on-w
  (implies (bit-equiv w w-equiv)
           (equal (!vex3-byte2->w$inline w x)
                  (!vex3-byte2->w$inline w-equiv x)))
  :rule-classes :congruence)

Theorem: !vex3-byte2->w$inline-of-vex3-byte2-fix-x

(defthm !vex3-byte2->w$inline-of-vex3-byte2-fix-x
  (equal (!vex3-byte2->w$inline w (vex3-byte2-fix x))
         (!vex3-byte2->w$inline w x)))

Theorem: !vex3-byte2->w$inline-vex3-byte2-equiv-congruence-on-x

(defthm !vex3-byte2->w$inline-vex3-byte2-equiv-congruence-on-x
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (!vex3-byte2->w$inline w x)
                  (!vex3-byte2->w$inline w x-equiv)))
  :rule-classes :congruence)

Theorem: !vex3-byte2->w-is-vex3-byte2

(defthm !vex3-byte2->w-is-vex3-byte2
  (equal (!vex3-byte2->w w x)
         (change-vex3-byte2 x :w w)))

Theorem: vex3-byte2->w-of-!vex3-byte2->w

(defthm vex3-byte2->w-of-!vex3-byte2->w
  (b* ((?new-x (!vex3-byte2->w$inline w x)))
    (equal (vex3-byte2->w new-x) (bfix w))))

Theorem: !vex3-byte2->w-equiv-under-mask

(defthm !vex3-byte2->w-equiv-under-mask
  (b* ((?new-x (!vex3-byte2->w$inline w x)))
    (vex3-byte2-equiv-under-mask new-x x 127)))

Function: vex3-byte2-debug$inline

(defun vex3-byte2-debug$inline (x)
  (declare (xargs :guard (vex3-byte2-p x)))
  (b* (((vex3-byte2 x)))
    (cons (cons 'pp x.pp)
          (cons (cons 'l x.l)
                (cons (cons 'vvvv x.vvvv)
                      (cons (cons 'w x.w) nil))))))

Function: vex-prefixes-map-p$inline

(defun vex-prefixes-map-p$inline (bytes vex-prefixes)
  (declare (type (unsigned-byte 16) bytes))
  (declare (xargs :guard (vex-prefixes-p vex-prefixes)))
  (declare (xargs :guard (and (vex-prefixes-byte0-p vex-prefixes)
                              (or (equal bytes 15)
                                  (equal bytes 3896)
                                  (equal bytes 3898)))))
  (b* ((byte0 (vex-prefixes->byte0 vex-prefixes))
       (byte1 (vex-prefixes->byte1 vex-prefixes)))
    (case bytes
      (15 (or (equal byte0 197)
              (and (equal byte0 196)
                   (equal (vex3-byte1->m-mmmm byte1) 1))))
      (otherwise (and (equal byte0 196)
                      (if (equal bytes 3896)
                          (equal (vex3-byte1->m-mmmm byte1) 2)
                        (equal (vex3-byte1->m-mmmm byte1)
                               3)))))))

Theorem: booleanp-of-vex-prefixes-map-p

(defthm booleanp-of-vex-prefixes-map-p
  (b* ((ok (vex-prefixes-map-p$inline bytes vex-prefixes)))
    (booleanp ok))
  :rule-classes :rewrite)

Function: vex->vvvv$inline

(defun vex->vvvv$inline (vex-prefixes)
  (declare (xargs :guard (vex-prefixes-p vex-prefixes)))
  (declare (xargs :guard (vex-prefixes-byte0-p vex-prefixes)))
  (case (vex-prefixes->byte0 vex-prefixes)
    (197 (vex2-byte1->vvvv (vex-prefixes->byte1 vex-prefixes)))
    (196 (vex3-byte2->vvvv (vex-prefixes->byte2 vex-prefixes)))
    (otherwise -1)))

Theorem: return-type-of-vex->vvvv

(defthm return-type-of-vex->vvvv
  (implies (vex-prefixes-byte0-p vex-prefixes)
           (b* ((vvvv (vex->vvvv$inline vex-prefixes)))
             (unsigned-byte-p 4 vvvv)))
  :rule-classes :rewrite)

Function: vex->l$inline

(defun vex->l$inline (vex-prefixes)
  (declare (type (unsigned-byte 24) vex-prefixes))
  (declare (xargs :guard (vex-prefixes-byte0-p vex-prefixes)))
  (case (vex-prefixes->byte0 vex-prefixes)
    (197 (vex2-byte1->l (vex-prefixes->byte1 vex-prefixes)))
    (196 (vex3-byte2->l (vex-prefixes->byte2 vex-prefixes)))
    (otherwise -1)))

Theorem: return-type-of-vex->l

(defthm return-type-of-vex->l
  (implies (vex-prefixes-byte0-p vex-prefixes)
           (b* ((l (vex->l$inline vex-prefixes)))
             (unsigned-byte-p 1 l)))
  :rule-classes :rewrite)

Function: vex->pp$inline

(defun vex->pp$inline (vex-prefixes)
  (declare (type (unsigned-byte 24) vex-prefixes))
  (declare (xargs :guard (vex-prefixes-byte0-p vex-prefixes)))
  (case (vex-prefixes->byte0 vex-prefixes)
    (197 (vex2-byte1->pp (vex-prefixes->byte1 vex-prefixes)))
    (196 (vex3-byte2->pp (vex-prefixes->byte2 vex-prefixes)))
    (otherwise -1)))

Theorem: return-type-of-vex->pp

(defthm return-type-of-vex->pp
  (implies (vex-prefixes-byte0-p vex-prefixes)
           (b* ((pp (vex->pp$inline vex-prefixes)))
             (unsigned-byte-p 2 pp)))
  :rule-classes :rewrite)

Function: vex->r$inline

(defun vex->r$inline (vex-prefixes)
  (declare (type (unsigned-byte 24) vex-prefixes))
  (declare (xargs :guard (vex-prefixes-byte0-p vex-prefixes)))
  (case (vex-prefixes->byte0 vex-prefixes)
    (197 (vex2-byte1->r (vex-prefixes->byte1 vex-prefixes)))
    (196 (vex3-byte1->r (vex-prefixes->byte1 vex-prefixes)))
    (otherwise -1)))

Theorem: return-type-of-vex->r

(defthm return-type-of-vex->r
  (implies (vex-prefixes-byte0-p vex-prefixes)
           (b* ((r (vex->r$inline vex-prefixes)))
             (unsigned-byte-p 1 r)))
  :rule-classes :rewrite)

Function: vex->w$inline

(defun vex->w$inline (vex-prefixes)
  (declare (type (unsigned-byte 24) vex-prefixes))
  (declare (xargs :guard (vex-prefixes-byte0-p vex-prefixes)))
  (case (vex-prefixes->byte0 vex-prefixes)
    (196 (vex3-byte2->w (vex-prefixes->byte2 vex-prefixes)))
    (otherwise 0)))

Theorem: return-type-of-vex->w

(defthm return-type-of-vex->w
  (implies (vex-prefixes-byte0-p vex-prefixes)
           (b* ((w (vex->w$inline vex-prefixes)))
             (unsigned-byte-p 1 w)))
  :rule-classes :rewrite)

Theorem: if-not-vex3-byte0-then-vex-w=0

(defthm if-not-vex3-byte0-then-vex-w=0
  (b* nil
    (implies (not (equal (vex-prefixes->byte0 vex-prefixes)
                         196))
             (equal (vex->w vex-prefixes) 0))))

Function: vex->x$inline

(defun vex->x$inline (vex-prefixes)
  (declare (xargs :guard (vex-prefixes-p vex-prefixes)))
  (case (vex-prefixes->byte0 vex-prefixes)
    (196 (vex3-byte1->x (vex-prefixes->byte1 vex-prefixes)))
    (otherwise 1)))

Function: vex->b$inline

(defun vex->b$inline (vex-prefixes)
  (declare (xargs :guard (vex-prefixes-p vex-prefixes)))
  (case (vex-prefixes->byte0 vex-prefixes)
    (196 (vex3-byte1->b (vex-prefixes->byte1 vex-prefixes)))
    (otherwise 1)))