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Structures

Evex-prefixes-layout-structures

Functions to decode and collect EVEX prefix bytes from an x86 instruction

Definitions and Theorems

Function: evex-prefixes-p$inline

(defun evex-prefixes-p$inline (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p 32 x)
       :exec (and (natp x) (< x 4294967296))))

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

(defthm evex-prefixes-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 32 x)
           (evex-prefixes-p x)))

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

(defthm unsigned-byte-p-when-evex-prefixes-p
  (implies (evex-prefixes-p x)
           (unsigned-byte-p 32 x)))

Theorem: evex-prefixes-p-compound-recognizer

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

Function: evex-prefixes-fix$inline

(defun evex-prefixes-fix$inline (x)
  (declare (xargs :guard (evex-prefixes-p x)))
  (mbe :logic (loghead 32 x) :exec x))

Theorem: evex-prefixes-p-of-evex-prefixes-fix

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

Theorem: evex-prefixes-fix-when-evex-prefixes-p

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

Function: evex-prefixes-equiv$inline

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

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

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

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

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

Theorem: evex-prefixes-fix-under-evex-prefixes-equiv

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

Function: evex-prefixes$inline

(defun evex-prefixes$inline (byte0 byte1 byte2 byte3)
  (declare (xargs :guard (and (8bits-p byte0)
                              (8bits-p byte1)
                              (8bits-p byte2)
                              (8bits-p byte3))))
  (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))
       (byte3 (mbe :logic (8bits-fix byte3)
                   :exec byte3)))
    (logapp 8 byte0
            (logapp 8 byte1 (logapp 8 byte2 byte3)))))

Theorem: evex-prefixes-p-of-evex-prefixes

(defthm evex-prefixes-p-of-evex-prefixes
  (b*
    ((evex-prefixes (evex-prefixes$inline byte0 byte1 byte2 byte3)))
    (evex-prefixes-p evex-prefixes))
  :rule-classes :rewrite)

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

(defthm evex-prefixes$inline-of-8bits-fix-byte0
  (equal (evex-prefixes$inline (8bits-fix byte0)
                               byte1 byte2 byte3)
         (evex-prefixes$inline byte0 byte1 byte2 byte3)))

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

(defthm evex-prefixes$inline-8bits-equiv-congruence-on-byte0
  (implies
       (8bits-equiv byte0 byte0-equiv)
       (equal (evex-prefixes$inline byte0 byte1 byte2 byte3)
              (evex-prefixes$inline byte0-equiv byte1 byte2 byte3)))
  :rule-classes :congruence)

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

(defthm evex-prefixes$inline-of-8bits-fix-byte1
  (equal (evex-prefixes$inline byte0 (8bits-fix byte1)
                               byte2 byte3)
         (evex-prefixes$inline byte0 byte1 byte2 byte3)))

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

(defthm evex-prefixes$inline-8bits-equiv-congruence-on-byte1
  (implies
       (8bits-equiv byte1 byte1-equiv)
       (equal (evex-prefixes$inline byte0 byte1 byte2 byte3)
              (evex-prefixes$inline byte0 byte1-equiv byte2 byte3)))
  :rule-classes :congruence)

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

(defthm evex-prefixes$inline-of-8bits-fix-byte2
  (equal (evex-prefixes$inline byte0 byte1 (8bits-fix byte2)
                               byte3)
         (evex-prefixes$inline byte0 byte1 byte2 byte3)))

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

(defthm evex-prefixes$inline-8bits-equiv-congruence-on-byte2
  (implies
       (8bits-equiv byte2 byte2-equiv)
       (equal (evex-prefixes$inline byte0 byte1 byte2 byte3)
              (evex-prefixes$inline byte0 byte1 byte2-equiv byte3)))
  :rule-classes :congruence)

Theorem: evex-prefixes$inline-of-8bits-fix-byte3

(defthm evex-prefixes$inline-of-8bits-fix-byte3
  (equal (evex-prefixes$inline byte0 byte1 byte2 (8bits-fix byte3))
         (evex-prefixes$inline byte0 byte1 byte2 byte3)))

Theorem: evex-prefixes$inline-8bits-equiv-congruence-on-byte3

(defthm evex-prefixes$inline-8bits-equiv-congruence-on-byte3
  (implies
       (8bits-equiv byte3 byte3-equiv)
       (equal (evex-prefixes$inline byte0 byte1 byte2 byte3)
              (evex-prefixes$inline byte0 byte1 byte2 byte3-equiv)))
  :rule-classes :congruence)

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

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

Function: evex-prefixes->byte0$inline

(defun evex-prefixes->byte0$inline (x)
  (declare (xargs :guard (evex-prefixes-p x)))
  (mbe :logic
       (let ((x (evex-prefixes-fix x)))
         (part-select x :low 0 :width 8))
       :exec (the (unsigned-byte 8)
                  (logand (the (unsigned-byte 8) 255)
                          (the (unsigned-byte 32) x)))))

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

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

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

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

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

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

Theorem: evex-prefixes->byte0-of-evex-prefixes

(defthm evex-prefixes->byte0-of-evex-prefixes
 (equal
      (evex-prefixes->byte0 (evex-prefixes byte0 byte1 byte2 byte3))
      (8bits-fix byte0)))

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

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

Function: evex-prefixes->byte1$inline

(defun evex-prefixes->byte1$inline (x)
 (declare (xargs :guard (evex-prefixes-p x)))
 (mbe
    :logic
    (let ((x (evex-prefixes-fix x)))
      (part-select x :low 8 :width 8))
    :exec (the (unsigned-byte 8)
               (logand (the (unsigned-byte 8) 255)
                       (the (unsigned-byte 24)
                            (ash (the (unsigned-byte 32) x) -8))))))

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

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

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

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

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

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

Theorem: evex-prefixes->byte1-of-evex-prefixes

(defthm evex-prefixes->byte1-of-evex-prefixes
 (equal
      (evex-prefixes->byte1 (evex-prefixes byte0 byte1 byte2 byte3))
      (8bits-fix byte1)))

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

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

Function: evex-prefixes->byte2$inline

(defun evex-prefixes->byte2$inline (x)
  (declare (xargs :guard (evex-prefixes-p x)))
  (mbe :logic
       (let ((x (evex-prefixes-fix x)))
         (part-select x :low 16 :width 8))
       :exec (the (unsigned-byte 8)
                  (logand (the (unsigned-byte 8) 255)
                          (the (unsigned-byte 16)
                               (ash (the (unsigned-byte 32) x)
                                    -16))))))

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

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

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

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

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

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

Theorem: evex-prefixes->byte2-of-evex-prefixes

(defthm evex-prefixes->byte2-of-evex-prefixes
 (equal
      (evex-prefixes->byte2 (evex-prefixes byte0 byte1 byte2 byte3))
      (8bits-fix byte2)))

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

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

Function: evex-prefixes->byte3$inline

(defun evex-prefixes->byte3$inline (x)
  (declare (xargs :guard (evex-prefixes-p x)))
  (mbe :logic
       (let ((x (evex-prefixes-fix x)))
         (part-select x :low 24 :width 8))
       :exec (the (unsigned-byte 8)
                  (logand (the (unsigned-byte 8) 255)
                          (the (unsigned-byte 8)
                               (ash (the (unsigned-byte 32) x)
                                    -24))))))

Theorem: 8bits-p-of-evex-prefixes->byte3

(defthm 8bits-p-of-evex-prefixes->byte3
  (b* ((byte3 (evex-prefixes->byte3$inline x)))
    (8bits-p byte3))
  :rule-classes :rewrite)

Theorem: evex-prefixes->byte3$inline-of-evex-prefixes-fix-x

(defthm evex-prefixes->byte3$inline-of-evex-prefixes-fix-x
  (equal (evex-prefixes->byte3$inline (evex-prefixes-fix x))
         (evex-prefixes->byte3$inline x)))

Theorem: evex-prefixes->byte3$inline-evex-prefixes-equiv-congruence-on-x

(defthm
    evex-prefixes->byte3$inline-evex-prefixes-equiv-congruence-on-x
  (implies (evex-prefixes-equiv x x-equiv)
           (equal (evex-prefixes->byte3$inline x)
                  (evex-prefixes->byte3$inline x-equiv)))
  :rule-classes :congruence)

Theorem: evex-prefixes->byte3-of-evex-prefixes

(defthm evex-prefixes->byte3-of-evex-prefixes
 (equal
      (evex-prefixes->byte3 (evex-prefixes byte0 byte1 byte2 byte3))
      (8bits-fix byte3)))

Theorem: evex-prefixes->byte3-of-write-with-mask

(defthm evex-prefixes->byte3-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x evex-prefixes-equiv-under-mask)
                (evex-prefixes-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 4278190080)
                       0))
           (equal (evex-prefixes->byte3 x)
                  (evex-prefixes->byte3 y))))

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

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

Function: !evex-prefixes->byte0$inline

(defun !evex-prefixes->byte0$inline (byte0 x)
  (declare (xargs :guard (and (8bits-p byte0)
                              (evex-prefixes-p x))))
  (mbe :logic
       (b* ((byte0 (mbe :logic (8bits-fix byte0)
                        :exec byte0))
            (x (evex-prefixes-fix x)))
         (part-install byte0 x :width 8 :low 0))
       :exec (the (unsigned-byte 32)
                  (logior (the (unsigned-byte 32)
                               (logand (the (unsigned-byte 32) x)
                                       (the (signed-byte 9) -256)))
                          (the (unsigned-byte 8) byte0)))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Function: !evex-prefixes->byte1$inline

(defun !evex-prefixes->byte1$inline (byte1 x)
 (declare (xargs :guard (and (8bits-p byte1)
                             (evex-prefixes-p x))))
 (mbe
     :logic
     (b* ((byte1 (mbe :logic (8bits-fix byte1)
                      :exec byte1))
          (x (evex-prefixes-fix x)))
       (part-install byte1 x :width 8 :low 8))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 17) -65281)))
                        (the (unsigned-byte 16)
                             (ash (the (unsigned-byte 8) byte1)
                                  8))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Function: !evex-prefixes->byte2$inline

(defun !evex-prefixes->byte2$inline (byte2 x)
 (declare (xargs :guard (and (8bits-p byte2)
                             (evex-prefixes-p x))))
 (mbe
  :logic
  (b* ((byte2 (mbe :logic (8bits-fix byte2)
                   :exec byte2))
       (x (evex-prefixes-fix x)))
    (part-install byte2 x :width 8 :low 16))
  :exec (the (unsigned-byte 32)
             (logior (the (unsigned-byte 32)
                          (logand (the (unsigned-byte 32) x)
                                  (the (signed-byte 25) -16711681)))
                     (the (unsigned-byte 24)
                          (ash (the (unsigned-byte 8) byte2)
                               16))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !evex-prefixes->byte2-equiv-under-mask
  (b* ((?new-x (!evex-prefixes->byte2$inline byte2 x)))
    (evex-prefixes-equiv-under-mask new-x x -16711681)))

Function: !evex-prefixes->byte3$inline

(defun !evex-prefixes->byte3$inline (byte3 x)
 (declare (xargs :guard (and (8bits-p byte3)
                             (evex-prefixes-p x))))
 (mbe :logic
      (b* ((byte3 (mbe :logic (8bits-fix byte3)
                       :exec byte3))
           (x (evex-prefixes-fix x)))
        (part-install byte3 x :width 8 :low 24))
      :exec
      (the (unsigned-byte 32)
           (logior (the (unsigned-byte 32)
                        (logand (the (unsigned-byte 32) x)
                                (the (signed-byte 33) -4278190081)))
                   (the (unsigned-byte 32)
                        (ash (the (unsigned-byte 8) byte3)
                             24))))))

Theorem: evex-prefixes-p-of-!evex-prefixes->byte3

(defthm evex-prefixes-p-of-!evex-prefixes->byte3
  (b* ((new-x (!evex-prefixes->byte3$inline byte3 x)))
    (evex-prefixes-p new-x))
  :rule-classes :rewrite)

Theorem: !evex-prefixes->byte3$inline-of-8bits-fix-byte3

(defthm !evex-prefixes->byte3$inline-of-8bits-fix-byte3
  (equal (!evex-prefixes->byte3$inline (8bits-fix byte3)
                                       x)
         (!evex-prefixes->byte3$inline byte3 x)))

Theorem: !evex-prefixes->byte3$inline-8bits-equiv-congruence-on-byte3

(defthm !evex-prefixes->byte3$inline-8bits-equiv-congruence-on-byte3
  (implies (8bits-equiv byte3 byte3-equiv)
           (equal (!evex-prefixes->byte3$inline byte3 x)
                  (!evex-prefixes->byte3$inline byte3-equiv x)))
  :rule-classes :congruence)

Theorem: !evex-prefixes->byte3$inline-of-evex-prefixes-fix-x

(defthm !evex-prefixes->byte3$inline-of-evex-prefixes-fix-x
  (equal (!evex-prefixes->byte3$inline byte3 (evex-prefixes-fix x))
         (!evex-prefixes->byte3$inline byte3 x)))

Theorem: !evex-prefixes->byte3$inline-evex-prefixes-equiv-congruence-on-x

(defthm
   !evex-prefixes->byte3$inline-evex-prefixes-equiv-congruence-on-x
  (implies (evex-prefixes-equiv x x-equiv)
           (equal (!evex-prefixes->byte3$inline byte3 x)
                  (!evex-prefixes->byte3$inline byte3 x-equiv)))
  :rule-classes :congruence)

Theorem: !evex-prefixes->byte3-is-evex-prefixes

(defthm !evex-prefixes->byte3-is-evex-prefixes
  (equal (!evex-prefixes->byte3 byte3 x)
         (change-evex-prefixes x :byte3 byte3)))

Theorem: evex-prefixes->byte3-of-!evex-prefixes->byte3

(defthm evex-prefixes->byte3-of-!evex-prefixes->byte3
  (b* ((?new-x (!evex-prefixes->byte3$inline byte3 x)))
    (equal (evex-prefixes->byte3 new-x)
           (8bits-fix byte3))))

Theorem: !evex-prefixes->byte3-equiv-under-mask

(defthm !evex-prefixes->byte3-equiv-under-mask
  (b* ((?new-x (!evex-prefixes->byte3$inline byte3 x)))
    (evex-prefixes-equiv-under-mask new-x x 16777215)))

Function: evex-prefixes-debug$inline

(defun evex-prefixes-debug$inline (x)
  (declare (xargs :guard (evex-prefixes-p x)))
  (b* (((evex-prefixes x)))
    (cons (cons 'byte0 x.byte0)
          (cons (cons 'byte1 x.byte1)
                (cons (cons 'byte2 x.byte2)
                      (cons (cons 'byte3 x.byte3) nil))))))

Function: evex-byte1-p$inline

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

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

(defthm evex-byte1-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 8 byte1)
           (evex-byte1-p byte1)))

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

(defthm unsigned-byte-p-when-evex-byte1-p
  (implies (evex-byte1-p byte1)
           (unsigned-byte-p 8 byte1)))

Theorem: evex-byte1-p-compound-recognizer

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

Function: evex-byte1-fix$inline

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

Theorem: evex-byte1-p-of-evex-byte1-fix

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

Theorem: evex-byte1-fix-when-evex-byte1-p

(defthm evex-byte1-fix-when-evex-byte1-p
  (implies (evex-byte1-p byte1)
           (equal (evex-byte1-fix byte1) byte1)))

Function: evex-byte1-equiv$inline

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

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

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

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

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

Theorem: evex-byte1-fix-under-evex-byte1-equiv

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

Function: evex-byte1$inline

(defun evex-byte1$inline (mm res r-prime b x r)
  (declare (xargs :guard (and (2bits-p mm)
                              (2bits-p res)
                              (bitp r-prime)
                              (bitp b)
                              (bitp x)
                              (bitp r))))
  (b* ((mm (mbe :logic (2bits-fix mm) :exec mm))
       (res (mbe :logic (2bits-fix res) :exec res))
       (r-prime (mbe :logic (bfix r-prime)
                     :exec r-prime))
       (b (mbe :logic (bfix b) :exec b))
       (x (mbe :logic (bfix x) :exec x))
       (r (mbe :logic (bfix r) :exec r)))
    (logapp 2 mm
            (logapp 2 res
                    (logapp 1
                            r-prime (logapp 1 b (logapp 1 x r)))))))

Theorem: evex-byte1-p-of-evex-byte1

(defthm evex-byte1-p-of-evex-byte1
  (b* ((evex-byte1 (evex-byte1$inline mm res r-prime b x r)))
    (evex-byte1-p evex-byte1))
  :rule-classes :rewrite)

Theorem: evex-byte1$inline-of-2bits-fix-mm

(defthm evex-byte1$inline-of-2bits-fix-mm
  (equal (evex-byte1$inline (2bits-fix mm)
                            res r-prime b x r)
         (evex-byte1$inline mm res r-prime b x r)))

Theorem: evex-byte1$inline-2bits-equiv-congruence-on-mm

(defthm evex-byte1$inline-2bits-equiv-congruence-on-mm
  (implies (2bits-equiv mm mm-equiv)
           (equal (evex-byte1$inline mm res r-prime b x r)
                  (evex-byte1$inline mm-equiv res r-prime b x r)))
  :rule-classes :congruence)

Theorem: evex-byte1$inline-of-2bits-fix-res

(defthm evex-byte1$inline-of-2bits-fix-res
  (equal (evex-byte1$inline mm (2bits-fix res)
                            r-prime b x r)
         (evex-byte1$inline mm res r-prime b x r)))

Theorem: evex-byte1$inline-2bits-equiv-congruence-on-res

(defthm evex-byte1$inline-2bits-equiv-congruence-on-res
  (implies (2bits-equiv res res-equiv)
           (equal (evex-byte1$inline mm res r-prime b x r)
                  (evex-byte1$inline mm res-equiv r-prime b x r)))
  :rule-classes :congruence)

Theorem: evex-byte1$inline-of-bfix-r-prime

(defthm evex-byte1$inline-of-bfix-r-prime
  (equal (evex-byte1$inline mm res (bfix r-prime)
                            b x r)
         (evex-byte1$inline mm res r-prime b x r)))

Theorem: evex-byte1$inline-bit-equiv-congruence-on-r-prime

(defthm evex-byte1$inline-bit-equiv-congruence-on-r-prime
  (implies (bit-equiv r-prime r-prime-equiv)
           (equal (evex-byte1$inline mm res r-prime b x r)
                  (evex-byte1$inline mm res r-prime-equiv b x r)))
  :rule-classes :congruence)

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

(defthm evex-byte1$inline-of-bfix-b
  (equal (evex-byte1$inline mm res r-prime (bfix b)
                            x r)
         (evex-byte1$inline mm res r-prime b x r)))

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

(defthm evex-byte1$inline-bit-equiv-congruence-on-b
  (implies (bit-equiv b b-equiv)
           (equal (evex-byte1$inline mm res r-prime b x r)
                  (evex-byte1$inline mm res r-prime b-equiv x r)))
  :rule-classes :congruence)

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

(defthm evex-byte1$inline-of-bfix-x
  (equal (evex-byte1$inline mm res r-prime b (bfix x)
                            r)
         (evex-byte1$inline mm res r-prime b x r)))

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

(defthm evex-byte1$inline-bit-equiv-congruence-on-x
  (implies (bit-equiv x x-equiv)
           (equal (evex-byte1$inline mm res r-prime b x r)
                  (evex-byte1$inline mm res r-prime b x-equiv r)))
  :rule-classes :congruence)

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

(defthm evex-byte1$inline-of-bfix-r
  (equal (evex-byte1$inline mm res r-prime b x (bfix r))
         (evex-byte1$inline mm res r-prime b x r)))

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

(defthm evex-byte1$inline-bit-equiv-congruence-on-r
  (implies (bit-equiv r r-equiv)
           (equal (evex-byte1$inline mm res r-prime b x r)
                  (evex-byte1$inline mm res r-prime b x r-equiv)))
  :rule-classes :congruence)

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

(defun evex-byte1-equiv-under-mask$inline (byte1 byte11 mask)
  (declare (xargs :guard (and (evex-byte1-p byte1)
                              (evex-byte1-p byte11)
                              (integerp mask))))
  (fty::int-equiv-under-mask (evex-byte1-fix byte1)
                             (evex-byte1-fix byte11)
                             mask))

Function: evex-byte1->mm$inline

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

Theorem: 2bits-p-of-evex-byte1->mm

(defthm 2bits-p-of-evex-byte1->mm
  (b* ((mm (evex-byte1->mm$inline byte1)))
    (2bits-p mm))
  :rule-classes :rewrite)

Theorem: evex-byte1->mm$inline-of-evex-byte1-fix-byte1

(defthm evex-byte1->mm$inline-of-evex-byte1-fix-byte1
  (equal (evex-byte1->mm$inline (evex-byte1-fix byte1))
         (evex-byte1->mm$inline byte1)))

Theorem: evex-byte1->mm$inline-evex-byte1-equiv-congruence-on-byte1

(defthm evex-byte1->mm$inline-evex-byte1-equiv-congruence-on-byte1
  (implies (evex-byte1-equiv byte1 byte1-equiv)
           (equal (evex-byte1->mm$inline byte1)
                  (evex-byte1->mm$inline byte1-equiv)))
  :rule-classes :congruence)

Theorem: evex-byte1->mm-of-evex-byte1

(defthm evex-byte1->mm-of-evex-byte1
  (equal (evex-byte1->mm (evex-byte1 mm res r-prime b x r))
         (2bits-fix mm)))

Theorem: evex-byte1->mm-of-write-with-mask

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

Function: evex-byte1->res$inline

(defun evex-byte1->res$inline (byte1)
  (declare (xargs :guard (evex-byte1-p byte1)))
  (mbe :logic
       (let ((byte1 (evex-byte1-fix byte1)))
         (part-select byte1 :low 2 :width 2))
       :exec (the (unsigned-byte 2)
                  (logand (the (unsigned-byte 2) 3)
                          (the (unsigned-byte 6)
                               (ash (the (unsigned-byte 8) byte1)
                                    -2))))))

Theorem: 2bits-p-of-evex-byte1->res

(defthm 2bits-p-of-evex-byte1->res
  (b* ((res (evex-byte1->res$inline byte1)))
    (2bits-p res))
  :rule-classes :rewrite)

Theorem: evex-byte1->res$inline-of-evex-byte1-fix-byte1

(defthm evex-byte1->res$inline-of-evex-byte1-fix-byte1
  (equal (evex-byte1->res$inline (evex-byte1-fix byte1))
         (evex-byte1->res$inline byte1)))

Theorem: evex-byte1->res$inline-evex-byte1-equiv-congruence-on-byte1

(defthm evex-byte1->res$inline-evex-byte1-equiv-congruence-on-byte1
  (implies (evex-byte1-equiv byte1 byte1-equiv)
           (equal (evex-byte1->res$inline byte1)
                  (evex-byte1->res$inline byte1-equiv)))
  :rule-classes :congruence)

Theorem: evex-byte1->res-of-evex-byte1

(defthm evex-byte1->res-of-evex-byte1
  (equal (evex-byte1->res (evex-byte1 mm res r-prime b x r))
         (2bits-fix res)))

Theorem: evex-byte1->res-of-write-with-mask

(defthm evex-byte1->res-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     byte1 evex-byte1-equiv-under-mask)
                (evex-byte1-equiv-under-mask byte1 y fty::mask)
                (equal (logand (lognot fty::mask) 12)
                       0))
           (equal (evex-byte1->res byte1)
                  (evex-byte1->res y))))

Function: evex-byte1->r-prime$inline

(defun evex-byte1->r-prime$inline (byte1)
  (declare (xargs :guard (evex-byte1-p byte1)))
  (mbe :logic
       (let ((byte1 (evex-byte1-fix byte1)))
         (part-select byte1 :low 4 :width 1))
       :exec (the (unsigned-byte 1)
                  (logand (the (unsigned-byte 1) 1)
                          (the (unsigned-byte 4)
                               (ash (the (unsigned-byte 8) byte1)
                                    -4))))))

Theorem: bitp-of-evex-byte1->r-prime

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

Theorem: evex-byte1->r-prime$inline-of-evex-byte1-fix-byte1

(defthm evex-byte1->r-prime$inline-of-evex-byte1-fix-byte1
  (equal (evex-byte1->r-prime$inline (evex-byte1-fix byte1))
         (evex-byte1->r-prime$inline byte1)))

Theorem: evex-byte1->r-prime$inline-evex-byte1-equiv-congruence-on-byte1

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

Theorem: evex-byte1->r-prime-of-evex-byte1

(defthm evex-byte1->r-prime-of-evex-byte1
  (equal (evex-byte1->r-prime (evex-byte1 mm res r-prime b x r))
         (bfix r-prime)))

Theorem: evex-byte1->r-prime-of-write-with-mask

(defthm evex-byte1->r-prime-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     byte1 evex-byte1-equiv-under-mask)
                (evex-byte1-equiv-under-mask byte1 y fty::mask)
                (equal (logand (lognot fty::mask) 16)
                       0))
           (equal (evex-byte1->r-prime byte1)
                  (evex-byte1->r-prime y))))

Function: evex-byte1->b$inline

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

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

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

Theorem: evex-byte1->b$inline-of-evex-byte1-fix-byte1

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

Theorem: evex-byte1->b$inline-evex-byte1-equiv-congruence-on-byte1

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

Theorem: evex-byte1->b-of-evex-byte1

(defthm evex-byte1->b-of-evex-byte1
  (equal (evex-byte1->b (evex-byte1 mm res r-prime b x r))
         (bfix b)))

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

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

Function: evex-byte1->x$inline

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

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

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

Theorem: evex-byte1->x$inline-of-evex-byte1-fix-byte1

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

Theorem: evex-byte1->x$inline-evex-byte1-equiv-congruence-on-byte1

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

Theorem: evex-byte1->x-of-evex-byte1

(defthm evex-byte1->x-of-evex-byte1
  (equal (evex-byte1->x (evex-byte1 mm res r-prime b x r))
         (bfix x)))

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

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

Function: evex-byte1->r$inline

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

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

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

Theorem: evex-byte1->r$inline-of-evex-byte1-fix-byte1

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

Theorem: evex-byte1->r$inline-evex-byte1-equiv-congruence-on-byte1

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

Theorem: evex-byte1->r-of-evex-byte1

(defthm evex-byte1->r-of-evex-byte1
  (equal (evex-byte1->r (evex-byte1 mm res r-prime b x r))
         (bfix r)))

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

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

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

(defthm evex-byte1-fix-in-terms-of-evex-byte1
  (equal (evex-byte1-fix byte1)
         (change-evex-byte1 byte1)))

Function: !evex-byte1->mm$inline

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

Theorem: evex-byte1-p-of-!evex-byte1->mm

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

Theorem: !evex-byte1->mm$inline-of-2bits-fix-mm

(defthm !evex-byte1->mm$inline-of-2bits-fix-mm
  (equal (!evex-byte1->mm$inline (2bits-fix mm)
                                 byte1)
         (!evex-byte1->mm$inline mm byte1)))

Theorem: !evex-byte1->mm$inline-2bits-equiv-congruence-on-mm

(defthm !evex-byte1->mm$inline-2bits-equiv-congruence-on-mm
  (implies (2bits-equiv mm mm-equiv)
           (equal (!evex-byte1->mm$inline mm byte1)
                  (!evex-byte1->mm$inline mm-equiv byte1)))
  :rule-classes :congruence)

Theorem: !evex-byte1->mm$inline-of-evex-byte1-fix-byte1

(defthm !evex-byte1->mm$inline-of-evex-byte1-fix-byte1
  (equal (!evex-byte1->mm$inline mm (evex-byte1-fix byte1))
         (!evex-byte1->mm$inline mm byte1)))

Theorem: !evex-byte1->mm$inline-evex-byte1-equiv-congruence-on-byte1

(defthm !evex-byte1->mm$inline-evex-byte1-equiv-congruence-on-byte1
  (implies (evex-byte1-equiv byte1 byte1-equiv)
           (equal (!evex-byte1->mm$inline mm byte1)
                  (!evex-byte1->mm$inline mm byte1-equiv)))
  :rule-classes :congruence)

Theorem: !evex-byte1->mm-is-evex-byte1

(defthm !evex-byte1->mm-is-evex-byte1
  (equal (!evex-byte1->mm mm byte1)
         (change-evex-byte1 byte1 :mm mm)))

Theorem: evex-byte1->mm-of-!evex-byte1->mm

(defthm evex-byte1->mm-of-!evex-byte1->mm
  (b* ((?new-byte1 (!evex-byte1->mm$inline mm byte1)))
    (equal (evex-byte1->mm new-byte1)
           (2bits-fix mm))))

Theorem: !evex-byte1->mm-equiv-under-mask

(defthm !evex-byte1->mm-equiv-under-mask
  (b* ((?new-byte1 (!evex-byte1->mm$inline mm byte1)))
    (evex-byte1-equiv-under-mask new-byte1 byte1 -4)))

Function: !evex-byte1->res$inline

(defun !evex-byte1->res$inline (res byte1)
 (declare (xargs :guard (and (2bits-p res)
                             (evex-byte1-p byte1))))
 (mbe
    :logic
    (b* ((res (mbe :logic (2bits-fix res) :exec res))
         (byte1 (evex-byte1-fix byte1)))
      (part-install res byte1
                    :width 2
                    :low 2))
    :exec (the (unsigned-byte 8)
               (logior (the (unsigned-byte 8)
                            (logand (the (unsigned-byte 8) byte1)
                                    (the (signed-byte 5) -13)))
                       (the (unsigned-byte 4)
                            (ash (the (unsigned-byte 2) res) 2))))))

Theorem: evex-byte1-p-of-!evex-byte1->res

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

Theorem: !evex-byte1->res$inline-of-2bits-fix-res

(defthm !evex-byte1->res$inline-of-2bits-fix-res
  (equal (!evex-byte1->res$inline (2bits-fix res)
                                  byte1)
         (!evex-byte1->res$inline res byte1)))

Theorem: !evex-byte1->res$inline-2bits-equiv-congruence-on-res

(defthm !evex-byte1->res$inline-2bits-equiv-congruence-on-res
  (implies (2bits-equiv res res-equiv)
           (equal (!evex-byte1->res$inline res byte1)
                  (!evex-byte1->res$inline res-equiv byte1)))
  :rule-classes :congruence)

Theorem: !evex-byte1->res$inline-of-evex-byte1-fix-byte1

(defthm !evex-byte1->res$inline-of-evex-byte1-fix-byte1
  (equal (!evex-byte1->res$inline res (evex-byte1-fix byte1))
         (!evex-byte1->res$inline res byte1)))

Theorem: !evex-byte1->res$inline-evex-byte1-equiv-congruence-on-byte1

(defthm !evex-byte1->res$inline-evex-byte1-equiv-congruence-on-byte1
  (implies (evex-byte1-equiv byte1 byte1-equiv)
           (equal (!evex-byte1->res$inline res byte1)
                  (!evex-byte1->res$inline res byte1-equiv)))
  :rule-classes :congruence)

Theorem: !evex-byte1->res-is-evex-byte1

(defthm !evex-byte1->res-is-evex-byte1
  (equal (!evex-byte1->res res byte1)
         (change-evex-byte1 byte1 :res res)))

Theorem: evex-byte1->res-of-!evex-byte1->res

(defthm evex-byte1->res-of-!evex-byte1->res
  (b* ((?new-byte1 (!evex-byte1->res$inline res byte1)))
    (equal (evex-byte1->res new-byte1)
           (2bits-fix res))))

Theorem: !evex-byte1->res-equiv-under-mask

(defthm !evex-byte1->res-equiv-under-mask
  (b* ((?new-byte1 (!evex-byte1->res$inline res byte1)))
    (evex-byte1-equiv-under-mask new-byte1 byte1 -13)))

Function: !evex-byte1->r-prime$inline

(defun !evex-byte1->r-prime$inline (r-prime byte1)
  (declare (xargs :guard (and (bitp r-prime)
                              (evex-byte1-p byte1))))
  (mbe :logic
       (b* ((r-prime (mbe :logic (bfix r-prime)
                          :exec r-prime))
            (byte1 (evex-byte1-fix byte1)))
         (part-install r-prime byte1
                       :width 1
                       :low 4))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) byte1)
                                       (the (signed-byte 6) -17)))
                          (the (unsigned-byte 5)
                               (ash (the (unsigned-byte 1) r-prime)
                                    4))))))

Theorem: evex-byte1-p-of-!evex-byte1->r-prime

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

Theorem: !evex-byte1->r-prime$inline-of-bfix-r-prime

(defthm !evex-byte1->r-prime$inline-of-bfix-r-prime
  (equal (!evex-byte1->r-prime$inline (bfix r-prime)
                                      byte1)
         (!evex-byte1->r-prime$inline r-prime byte1)))

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

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

Theorem: !evex-byte1->r-prime$inline-of-evex-byte1-fix-byte1

(defthm !evex-byte1->r-prime$inline-of-evex-byte1-fix-byte1
 (equal (!evex-byte1->r-prime$inline r-prime (evex-byte1-fix byte1))
        (!evex-byte1->r-prime$inline r-prime byte1)))

Theorem: !evex-byte1->r-prime$inline-evex-byte1-equiv-congruence-on-byte1

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

Theorem: !evex-byte1->r-prime-is-evex-byte1

(defthm !evex-byte1->r-prime-is-evex-byte1
  (equal (!evex-byte1->r-prime r-prime byte1)
         (change-evex-byte1 byte1
                            :r-prime r-prime)))

Theorem: evex-byte1->r-prime-of-!evex-byte1->r-prime

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

Theorem: !evex-byte1->r-prime-equiv-under-mask

(defthm !evex-byte1->r-prime-equiv-under-mask
  (b* ((?new-byte1 (!evex-byte1->r-prime$inline r-prime byte1)))
    (evex-byte1-equiv-under-mask new-byte1 byte1 -17)))

Function: !evex-byte1->b$inline

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

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

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

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

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

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

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

Theorem: !evex-byte1->b$inline-of-evex-byte1-fix-byte1

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

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

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

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

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

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

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

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

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

Function: !evex-byte1->x$inline

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

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

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

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

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

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

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

Theorem: !evex-byte1->x$inline-of-evex-byte1-fix-byte1

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

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

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

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

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

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

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

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

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

Function: !evex-byte1->r$inline

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

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

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

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

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

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

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

Theorem: !evex-byte1->r$inline-of-evex-byte1-fix-byte1

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

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

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

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

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

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

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

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

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

Function: evex-byte1-debug$inline

(defun evex-byte1-debug$inline (byte1)
 (declare (xargs :guard (evex-byte1-p byte1)))
 (b* (((evex-byte1 byte1)))
   (cons (cons 'mm byte1.mm)
         (cons (cons 'res byte1.res)
               (cons (cons 'r-prime byte1.r-prime)
                     (cons (cons 'b byte1.b)
                           (cons (cons 'x byte1.x)
                                 (cons (cons 'r byte1.r) nil))))))))

Function: evex-byte2-p$inline

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

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

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

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

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

Theorem: evex-byte2-p-compound-recognizer

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

Function: evex-byte2-fix$inline

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

Theorem: evex-byte2-p-of-evex-byte2-fix

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

Theorem: evex-byte2-fix-when-evex-byte2-p

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

Function: evex-byte2-equiv$inline

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

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

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

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

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

Theorem: evex-byte2-fix-under-evex-byte2-equiv

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

Function: evex-byte2$inline

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

Theorem: evex-byte2-p-of-evex-byte2

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

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

(defthm evex-byte2$inline-of-2bits-fix-pp
  (equal (evex-byte2$inline (2bits-fix pp)
                            res vvvv w)
         (evex-byte2$inline pp res vvvv w)))

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

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

Theorem: evex-byte2$inline-of-bfix-res

(defthm evex-byte2$inline-of-bfix-res
  (equal (evex-byte2$inline pp (bfix res) vvvv w)
         (evex-byte2$inline pp res vvvv w)))

Theorem: evex-byte2$inline-bit-equiv-congruence-on-res

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

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

(defthm evex-byte2$inline-of-4bits-fix-vvvv
  (equal (evex-byte2$inline pp res (4bits-fix vvvv)
                            w)
         (evex-byte2$inline pp res vvvv w)))

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

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

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

(defthm evex-byte2$inline-of-bfix-w
  (equal (evex-byte2$inline pp res vvvv (bfix w))
         (evex-byte2$inline pp res vvvv w)))

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

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

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

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

Function: evex-byte2->pp$inline

(defun evex-byte2->pp$inline (x)
  (declare (xargs :guard (evex-byte2-p x)))
  (mbe :logic
       (let ((x (evex-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-evex-byte2->pp

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

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

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

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

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

Theorem: evex-byte2->pp-of-evex-byte2

(defthm evex-byte2->pp-of-evex-byte2
  (equal (evex-byte2->pp (evex-byte2 pp res vvvv w))
         (2bits-fix pp)))

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

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

Function: evex-byte2->res$inline

(defun evex-byte2->res$inline (x)
 (declare (xargs :guard (evex-byte2-p x)))
 (mbe
     :logic
     (let ((x (evex-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-evex-byte2->res

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

Theorem: evex-byte2->res$inline-of-evex-byte2-fix-x

(defthm evex-byte2->res$inline-of-evex-byte2-fix-x
  (equal (evex-byte2->res$inline (evex-byte2-fix x))
         (evex-byte2->res$inline x)))

Theorem: evex-byte2->res$inline-evex-byte2-equiv-congruence-on-x

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

Theorem: evex-byte2->res-of-evex-byte2

(defthm evex-byte2->res-of-evex-byte2
  (equal (evex-byte2->res (evex-byte2 pp res vvvv w))
         (bfix res)))

Theorem: evex-byte2->res-of-write-with-mask

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

Function: evex-byte2->vvvv$inline

(defun evex-byte2->vvvv$inline (x)
 (declare (xargs :guard (evex-byte2-p x)))
 (mbe
     :logic
     (let ((x (evex-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-evex-byte2->vvvv

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

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

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

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

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

Theorem: evex-byte2->vvvv-of-evex-byte2

(defthm evex-byte2->vvvv-of-evex-byte2
  (equal (evex-byte2->vvvv (evex-byte2 pp res vvvv w))
         (4bits-fix vvvv)))

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

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

Function: evex-byte2->w$inline

(defun evex-byte2->w$inline (x)
 (declare (xargs :guard (evex-byte2-p x)))
 (mbe
     :logic
     (let ((x (evex-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-evex-byte2->w

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

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

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

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

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

Theorem: evex-byte2->w-of-evex-byte2

(defthm evex-byte2->w-of-evex-byte2
  (equal (evex-byte2->w (evex-byte2 pp res vvvv w))
         (bfix w)))

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

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

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

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

Function: !evex-byte2->pp$inline

(defun !evex-byte2->pp$inline (pp x)
  (declare (xargs :guard (and (2bits-p pp) (evex-byte2-p x))))
  (mbe :logic
       (b* ((pp (mbe :logic (2bits-fix pp) :exec pp))
            (x (evex-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: evex-byte2-p-of-!evex-byte2->pp

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Function: !evex-byte2->res$inline

(defun !evex-byte2->res$inline (res x)
 (declare (xargs :guard (and (bitp res) (evex-byte2-p x))))
 (mbe
    :logic
    (b* ((res (mbe :logic (bfix res) :exec res))
         (x (evex-byte2-fix x)))
      (part-install res 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) res) 2))))))

Theorem: evex-byte2-p-of-!evex-byte2->res

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

Theorem: !evex-byte2->res$inline-of-bfix-res

(defthm !evex-byte2->res$inline-of-bfix-res
  (equal (!evex-byte2->res$inline (bfix res) x)
         (!evex-byte2->res$inline res x)))

Theorem: !evex-byte2->res$inline-bit-equiv-congruence-on-res

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

Theorem: !evex-byte2->res$inline-of-evex-byte2-fix-x

(defthm !evex-byte2->res$inline-of-evex-byte2-fix-x
  (equal (!evex-byte2->res$inline res (evex-byte2-fix x))
         (!evex-byte2->res$inline res x)))

Theorem: !evex-byte2->res$inline-evex-byte2-equiv-congruence-on-x

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

Theorem: !evex-byte2->res-is-evex-byte2

(defthm !evex-byte2->res-is-evex-byte2
  (equal (!evex-byte2->res res x)
         (change-evex-byte2 x :res res)))

Theorem: evex-byte2->res-of-!evex-byte2->res

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

Theorem: !evex-byte2->res-equiv-under-mask

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

Function: !evex-byte2->vvvv$inline

(defun !evex-byte2->vvvv$inline (vvvv x)
  (declare (xargs :guard (and (4bits-p vvvv) (evex-byte2-p x))))
  (mbe :logic
       (b* ((vvvv (mbe :logic (4bits-fix vvvv)
                       :exec vvvv))
            (x (evex-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: evex-byte2-p-of-!evex-byte2->vvvv

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Function: !evex-byte2->w$inline

(defun !evex-byte2->w$inline (w x)
 (declare (xargs :guard (and (bitp w) (evex-byte2-p x))))
 (mbe :logic
      (b* ((w (mbe :logic (bfix w) :exec w))
           (x (evex-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: evex-byte2-p-of-!evex-byte2->w

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Function: evex-byte2-debug$inline

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

Function: evex-byte3-p$inline

(defun evex-byte3-p$inline (x)
  (declare (xargs :guard t))
  (mbe :logic (unsigned-byte-p 8 x)
       :exec (and (natp x) (< x 256))))

Theorem: evex-byte3-p-when-unsigned-byte-p

(defthm evex-byte3-p-when-unsigned-byte-p
  (implies (unsigned-byte-p 8 x)
           (evex-byte3-p x)))

Theorem: unsigned-byte-p-when-evex-byte3-p

(defthm unsigned-byte-p-when-evex-byte3-p
  (implies (evex-byte3-p x)
           (unsigned-byte-p 8 x)))

Theorem: evex-byte3-p-compound-recognizer

(defthm evex-byte3-p-compound-recognizer
  (implies (evex-byte3-p x) (natp x))
  :rule-classes :compound-recognizer)

Function: evex-byte3-fix$inline

(defun evex-byte3-fix$inline (x)
  (declare (xargs :guard (evex-byte3-p x)))
  (mbe :logic (loghead 8 x) :exec x))

Theorem: evex-byte3-p-of-evex-byte3-fix

(defthm evex-byte3-p-of-evex-byte3-fix
  (b* ((fty::fixed (evex-byte3-fix$inline x)))
    (evex-byte3-p fty::fixed))
  :rule-classes :rewrite)

Theorem: evex-byte3-fix-when-evex-byte3-p

(defthm evex-byte3-fix-when-evex-byte3-p
  (implies (evex-byte3-p x)
           (equal (evex-byte3-fix x) x)))

Function: evex-byte3-equiv$inline

(defun evex-byte3-equiv$inline (x y)
  (declare (xargs :guard (and (evex-byte3-p x)
                              (evex-byte3-p y))))
  (equal (evex-byte3-fix x)
         (evex-byte3-fix y)))

Theorem: evex-byte3-equiv-is-an-equivalence

(defthm evex-byte3-equiv-is-an-equivalence
  (and (booleanp (evex-byte3-equiv x y))
       (evex-byte3-equiv x x)
       (implies (evex-byte3-equiv x y)
                (evex-byte3-equiv y x))
       (implies (and (evex-byte3-equiv x y)
                     (evex-byte3-equiv y z))
                (evex-byte3-equiv x z)))
  :rule-classes (:equivalence))

Theorem: evex-byte3-equiv-implies-equal-evex-byte3-fix-1

(defthm evex-byte3-equiv-implies-equal-evex-byte3-fix-1
  (implies (evex-byte3-equiv x x-equiv)
           (equal (evex-byte3-fix x)
                  (evex-byte3-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: evex-byte3-fix-under-evex-byte3-equiv

(defthm evex-byte3-fix-under-evex-byte3-equiv
  (evex-byte3-equiv (evex-byte3-fix x) x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Function: evex-byte3$inline

(defun evex-byte3$inline (aaa v-prime b vl/rc z)
  (declare (xargs :guard (and (3bits-p aaa)
                              (bitp v-prime)
                              (bitp b)
                              (2bits-p vl/rc)
                              (bitp z))))
  (b* ((aaa (mbe :logic (3bits-fix aaa) :exec aaa))
       (v-prime (mbe :logic (bfix v-prime)
                     :exec v-prime))
       (b (mbe :logic (bfix b) :exec b))
       (vl/rc (mbe :logic (2bits-fix vl/rc)
                   :exec vl/rc))
       (z (mbe :logic (bfix z) :exec z)))
    (logapp 3 aaa
            (logapp 1 v-prime
                    (logapp 1 b (logapp 2 vl/rc z))))))

Theorem: evex-byte3-p-of-evex-byte3

(defthm evex-byte3-p-of-evex-byte3
  (b* ((evex-byte3 (evex-byte3$inline aaa v-prime b vl/rc z)))
    (evex-byte3-p evex-byte3))
  :rule-classes :rewrite)

Theorem: evex-byte3$inline-of-3bits-fix-aaa

(defthm evex-byte3$inline-of-3bits-fix-aaa
  (equal (evex-byte3$inline (3bits-fix aaa)
                            v-prime b vl/rc z)
         (evex-byte3$inline aaa v-prime b vl/rc z)))

Theorem: evex-byte3$inline-3bits-equiv-congruence-on-aaa

(defthm evex-byte3$inline-3bits-equiv-congruence-on-aaa
  (implies (3bits-equiv aaa aaa-equiv)
           (equal (evex-byte3$inline aaa v-prime b vl/rc z)
                  (evex-byte3$inline aaa-equiv v-prime b vl/rc z)))
  :rule-classes :congruence)

Theorem: evex-byte3$inline-of-bfix-v-prime

(defthm evex-byte3$inline-of-bfix-v-prime
  (equal (evex-byte3$inline aaa (bfix v-prime)
                            b vl/rc z)
         (evex-byte3$inline aaa v-prime b vl/rc z)))

Theorem: evex-byte3$inline-bit-equiv-congruence-on-v-prime

(defthm evex-byte3$inline-bit-equiv-congruence-on-v-prime
  (implies (bit-equiv v-prime v-prime-equiv)
           (equal (evex-byte3$inline aaa v-prime b vl/rc z)
                  (evex-byte3$inline aaa v-prime-equiv b vl/rc z)))
  :rule-classes :congruence)

Theorem: evex-byte3$inline-of-bfix-b

(defthm evex-byte3$inline-of-bfix-b
  (equal (evex-byte3$inline aaa v-prime (bfix b)
                            vl/rc z)
         (evex-byte3$inline aaa v-prime b vl/rc z)))

Theorem: evex-byte3$inline-bit-equiv-congruence-on-b

(defthm evex-byte3$inline-bit-equiv-congruence-on-b
  (implies (bit-equiv b b-equiv)
           (equal (evex-byte3$inline aaa v-prime b vl/rc z)
                  (evex-byte3$inline aaa v-prime b-equiv vl/rc z)))
  :rule-classes :congruence)

Theorem: evex-byte3$inline-of-2bits-fix-vl/rc

(defthm evex-byte3$inline-of-2bits-fix-vl/rc
  (equal (evex-byte3$inline aaa v-prime b (2bits-fix vl/rc)
                            z)
         (evex-byte3$inline aaa v-prime b vl/rc z)))

Theorem: evex-byte3$inline-2bits-equiv-congruence-on-vl/rc

(defthm evex-byte3$inline-2bits-equiv-congruence-on-vl/rc
  (implies (2bits-equiv vl/rc vl/rc-equiv)
           (equal (evex-byte3$inline aaa v-prime b vl/rc z)
                  (evex-byte3$inline aaa v-prime b vl/rc-equiv z)))
  :rule-classes :congruence)

Theorem: evex-byte3$inline-of-bfix-z

(defthm evex-byte3$inline-of-bfix-z
  (equal (evex-byte3$inline aaa v-prime b vl/rc (bfix z))
         (evex-byte3$inline aaa v-prime b vl/rc z)))

Theorem: evex-byte3$inline-bit-equiv-congruence-on-z

(defthm evex-byte3$inline-bit-equiv-congruence-on-z
  (implies (bit-equiv z z-equiv)
           (equal (evex-byte3$inline aaa v-prime b vl/rc z)
                  (evex-byte3$inline aaa v-prime b vl/rc z-equiv)))
  :rule-classes :congruence)

Function: evex-byte3-equiv-under-mask$inline

(defun evex-byte3-equiv-under-mask$inline (x x1 mask)
  (declare (xargs :guard (and (evex-byte3-p x)
                              (evex-byte3-p x1)
                              (integerp mask))))
  (fty::int-equiv-under-mask (evex-byte3-fix x)
                             (evex-byte3-fix x1)
                             mask))

Function: evex-byte3->aaa$inline

(defun evex-byte3->aaa$inline (x)
  (declare (xargs :guard (evex-byte3-p x)))
  (mbe :logic
       (let ((x (evex-byte3-fix x)))
         (part-select x :low 0 :width 3))
       :exec (the (unsigned-byte 3)
                  (logand (the (unsigned-byte 3) 7)
                          (the (unsigned-byte 8) x)))))

Theorem: 3bits-p-of-evex-byte3->aaa

(defthm 3bits-p-of-evex-byte3->aaa
  (b* ((aaa (evex-byte3->aaa$inline x)))
    (3bits-p aaa))
  :rule-classes :rewrite)

Theorem: evex-byte3->aaa$inline-of-evex-byte3-fix-x

(defthm evex-byte3->aaa$inline-of-evex-byte3-fix-x
  (equal (evex-byte3->aaa$inline (evex-byte3-fix x))
         (evex-byte3->aaa$inline x)))

Theorem: evex-byte3->aaa$inline-evex-byte3-equiv-congruence-on-x

(defthm evex-byte3->aaa$inline-evex-byte3-equiv-congruence-on-x
  (implies (evex-byte3-equiv x x-equiv)
           (equal (evex-byte3->aaa$inline x)
                  (evex-byte3->aaa$inline x-equiv)))
  :rule-classes :congruence)

Theorem: evex-byte3->aaa-of-evex-byte3

(defthm evex-byte3->aaa-of-evex-byte3
  (equal (evex-byte3->aaa (evex-byte3 aaa v-prime b vl/rc z))
         (3bits-fix aaa)))

Theorem: evex-byte3->aaa-of-write-with-mask

(defthm evex-byte3->aaa-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x evex-byte3-equiv-under-mask)
                (evex-byte3-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 7) 0))
           (equal (evex-byte3->aaa x)
                  (evex-byte3->aaa y))))

Function: evex-byte3->v-prime$inline

(defun evex-byte3->v-prime$inline (x)
 (declare (xargs :guard (evex-byte3-p x)))
 (mbe
     :logic
     (let ((x (evex-byte3-fix x)))
       (part-select x :low 3 :width 1))
     :exec (the (unsigned-byte 1)
                (logand (the (unsigned-byte 1) 1)
                        (the (unsigned-byte 5)
                             (ash (the (unsigned-byte 8) x) -3))))))

Theorem: bitp-of-evex-byte3->v-prime

(defthm bitp-of-evex-byte3->v-prime
  (b* ((v-prime (evex-byte3->v-prime$inline x)))
    (bitp v-prime))
  :rule-classes :rewrite)

Theorem: evex-byte3->v-prime$inline-of-evex-byte3-fix-x

(defthm evex-byte3->v-prime$inline-of-evex-byte3-fix-x
  (equal (evex-byte3->v-prime$inline (evex-byte3-fix x))
         (evex-byte3->v-prime$inline x)))

Theorem: evex-byte3->v-prime$inline-evex-byte3-equiv-congruence-on-x

(defthm evex-byte3->v-prime$inline-evex-byte3-equiv-congruence-on-x
  (implies (evex-byte3-equiv x x-equiv)
           (equal (evex-byte3->v-prime$inline x)
                  (evex-byte3->v-prime$inline x-equiv)))
  :rule-classes :congruence)

Theorem: evex-byte3->v-prime-of-evex-byte3

(defthm evex-byte3->v-prime-of-evex-byte3
  (equal (evex-byte3->v-prime (evex-byte3 aaa v-prime b vl/rc z))
         (bfix v-prime)))

Theorem: evex-byte3->v-prime-of-write-with-mask

(defthm evex-byte3->v-prime-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x evex-byte3-equiv-under-mask)
                (evex-byte3-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 8) 0))
           (equal (evex-byte3->v-prime x)
                  (evex-byte3->v-prime y))))

Function: evex-byte3->b$inline

(defun evex-byte3->b$inline (x)
 (declare (xargs :guard (evex-byte3-p x)))
 (mbe
     :logic
     (let ((x (evex-byte3-fix x)))
       (part-select x :low 4 :width 1))
     :exec (the (unsigned-byte 1)
                (logand (the (unsigned-byte 1) 1)
                        (the (unsigned-byte 4)
                             (ash (the (unsigned-byte 8) x) -4))))))

Theorem: bitp-of-evex-byte3->b

(defthm bitp-of-evex-byte3->b
  (b* ((b (evex-byte3->b$inline x)))
    (bitp b))
  :rule-classes :rewrite)

Theorem: evex-byte3->b$inline-of-evex-byte3-fix-x

(defthm evex-byte3->b$inline-of-evex-byte3-fix-x
  (equal (evex-byte3->b$inline (evex-byte3-fix x))
         (evex-byte3->b$inline x)))

Theorem: evex-byte3->b$inline-evex-byte3-equiv-congruence-on-x

(defthm evex-byte3->b$inline-evex-byte3-equiv-congruence-on-x
  (implies (evex-byte3-equiv x x-equiv)
           (equal (evex-byte3->b$inline x)
                  (evex-byte3->b$inline x-equiv)))
  :rule-classes :congruence)

Theorem: evex-byte3->b-of-evex-byte3

(defthm evex-byte3->b-of-evex-byte3
  (equal (evex-byte3->b (evex-byte3 aaa v-prime b vl/rc z))
         (bfix b)))

Theorem: evex-byte3->b-of-write-with-mask

(defthm evex-byte3->b-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x evex-byte3-equiv-under-mask)
                (evex-byte3-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 16)
                       0))
           (equal (evex-byte3->b x)
                  (evex-byte3->b y))))

Function: evex-byte3->vl/rc$inline

(defun evex-byte3->vl/rc$inline (x)
 (declare (xargs :guard (evex-byte3-p x)))
 (mbe
     :logic
     (let ((x (evex-byte3-fix x)))
       (part-select x :low 5 :width 2))
     :exec (the (unsigned-byte 2)
                (logand (the (unsigned-byte 2) 3)
                        (the (unsigned-byte 3)
                             (ash (the (unsigned-byte 8) x) -5))))))

Theorem: 2bits-p-of-evex-byte3->vl/rc

(defthm 2bits-p-of-evex-byte3->vl/rc
  (b* ((vl/rc (evex-byte3->vl/rc$inline x)))
    (2bits-p vl/rc))
  :rule-classes :rewrite)

Theorem: evex-byte3->vl/rc$inline-of-evex-byte3-fix-x

(defthm evex-byte3->vl/rc$inline-of-evex-byte3-fix-x
  (equal (evex-byte3->vl/rc$inline (evex-byte3-fix x))
         (evex-byte3->vl/rc$inline x)))

Theorem: evex-byte3->vl/rc$inline-evex-byte3-equiv-congruence-on-x

(defthm evex-byte3->vl/rc$inline-evex-byte3-equiv-congruence-on-x
  (implies (evex-byte3-equiv x x-equiv)
           (equal (evex-byte3->vl/rc$inline x)
                  (evex-byte3->vl/rc$inline x-equiv)))
  :rule-classes :congruence)

Theorem: evex-byte3->vl/rc-of-evex-byte3

(defthm evex-byte3->vl/rc-of-evex-byte3
  (equal (evex-byte3->vl/rc (evex-byte3 aaa v-prime b vl/rc z))
         (2bits-fix vl/rc)))

Theorem: evex-byte3->vl/rc-of-write-with-mask

(defthm evex-byte3->vl/rc-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x evex-byte3-equiv-under-mask)
                (evex-byte3-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 96)
                       0))
           (equal (evex-byte3->vl/rc x)
                  (evex-byte3->vl/rc y))))

Function: evex-byte3->z$inline

(defun evex-byte3->z$inline (x)
 (declare (xargs :guard (evex-byte3-p x)))
 (mbe
     :logic
     (let ((x (evex-byte3-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-evex-byte3->z

(defthm bitp-of-evex-byte3->z
  (b* ((z (evex-byte3->z$inline x)))
    (bitp z))
  :rule-classes :rewrite)

Theorem: evex-byte3->z$inline-of-evex-byte3-fix-x

(defthm evex-byte3->z$inline-of-evex-byte3-fix-x
  (equal (evex-byte3->z$inline (evex-byte3-fix x))
         (evex-byte3->z$inline x)))

Theorem: evex-byte3->z$inline-evex-byte3-equiv-congruence-on-x

(defthm evex-byte3->z$inline-evex-byte3-equiv-congruence-on-x
  (implies (evex-byte3-equiv x x-equiv)
           (equal (evex-byte3->z$inline x)
                  (evex-byte3->z$inline x-equiv)))
  :rule-classes :congruence)

Theorem: evex-byte3->z-of-evex-byte3

(defthm evex-byte3->z-of-evex-byte3
  (equal (evex-byte3->z (evex-byte3 aaa v-prime b vl/rc z))
         (bfix z)))

Theorem: evex-byte3->z-of-write-with-mask

(defthm evex-byte3->z-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x evex-byte3-equiv-under-mask)
                (evex-byte3-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 128)
                       0))
           (equal (evex-byte3->z x)
                  (evex-byte3->z y))))

Theorem: evex-byte3-fix-in-terms-of-evex-byte3

(defthm evex-byte3-fix-in-terms-of-evex-byte3
  (equal (evex-byte3-fix x)
         (change-evex-byte3 x)))

Function: !evex-byte3->aaa$inline

(defun !evex-byte3->aaa$inline (aaa x)
  (declare (xargs :guard (and (3bits-p aaa) (evex-byte3-p x))))
  (mbe :logic
       (b* ((aaa (mbe :logic (3bits-fix aaa) :exec aaa))
            (x (evex-byte3-fix x)))
         (part-install aaa x :width 3 :low 0))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 4) -8)))
                          (the (unsigned-byte 3) aaa)))))

Theorem: evex-byte3-p-of-!evex-byte3->aaa

(defthm evex-byte3-p-of-!evex-byte3->aaa
  (b* ((new-x (!evex-byte3->aaa$inline aaa x)))
    (evex-byte3-p new-x))
  :rule-classes :rewrite)

Theorem: !evex-byte3->aaa$inline-of-3bits-fix-aaa

(defthm !evex-byte3->aaa$inline-of-3bits-fix-aaa
  (equal (!evex-byte3->aaa$inline (3bits-fix aaa)
                                  x)
         (!evex-byte3->aaa$inline aaa x)))

Theorem: !evex-byte3->aaa$inline-3bits-equiv-congruence-on-aaa

(defthm !evex-byte3->aaa$inline-3bits-equiv-congruence-on-aaa
  (implies (3bits-equiv aaa aaa-equiv)
           (equal (!evex-byte3->aaa$inline aaa x)
                  (!evex-byte3->aaa$inline aaa-equiv x)))
  :rule-classes :congruence)

Theorem: !evex-byte3->aaa$inline-of-evex-byte3-fix-x

(defthm !evex-byte3->aaa$inline-of-evex-byte3-fix-x
  (equal (!evex-byte3->aaa$inline aaa (evex-byte3-fix x))
         (!evex-byte3->aaa$inline aaa x)))

Theorem: !evex-byte3->aaa$inline-evex-byte3-equiv-congruence-on-x

(defthm !evex-byte3->aaa$inline-evex-byte3-equiv-congruence-on-x
  (implies (evex-byte3-equiv x x-equiv)
           (equal (!evex-byte3->aaa$inline aaa x)
                  (!evex-byte3->aaa$inline aaa x-equiv)))
  :rule-classes :congruence)

Theorem: !evex-byte3->aaa-is-evex-byte3

(defthm !evex-byte3->aaa-is-evex-byte3
  (equal (!evex-byte3->aaa aaa x)
         (change-evex-byte3 x :aaa aaa)))

Theorem: evex-byte3->aaa-of-!evex-byte3->aaa

(defthm evex-byte3->aaa-of-!evex-byte3->aaa
  (b* ((?new-x (!evex-byte3->aaa$inline aaa x)))
    (equal (evex-byte3->aaa new-x)
           (3bits-fix aaa))))

Theorem: !evex-byte3->aaa-equiv-under-mask

(defthm !evex-byte3->aaa-equiv-under-mask
  (b* ((?new-x (!evex-byte3->aaa$inline aaa x)))
    (evex-byte3-equiv-under-mask new-x x -8)))

Function: !evex-byte3->v-prime$inline

(defun !evex-byte3->v-prime$inline (v-prime x)
  (declare (xargs :guard (and (bitp v-prime) (evex-byte3-p x))))
  (mbe :logic
       (b* ((v-prime (mbe :logic (bfix v-prime)
                          :exec v-prime))
            (x (evex-byte3-fix x)))
         (part-install v-prime x
                       :width 1
                       :low 3))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 5) -9)))
                          (the (unsigned-byte 4)
                               (ash (the (unsigned-byte 1) v-prime)
                                    3))))))

Theorem: evex-byte3-p-of-!evex-byte3->v-prime

(defthm evex-byte3-p-of-!evex-byte3->v-prime
  (b* ((new-x (!evex-byte3->v-prime$inline v-prime x)))
    (evex-byte3-p new-x))
  :rule-classes :rewrite)

Theorem: !evex-byte3->v-prime$inline-of-bfix-v-prime

(defthm !evex-byte3->v-prime$inline-of-bfix-v-prime
  (equal (!evex-byte3->v-prime$inline (bfix v-prime)
                                      x)
         (!evex-byte3->v-prime$inline v-prime x)))

Theorem: !evex-byte3->v-prime$inline-bit-equiv-congruence-on-v-prime

(defthm !evex-byte3->v-prime$inline-bit-equiv-congruence-on-v-prime
  (implies (bit-equiv v-prime v-prime-equiv)
           (equal (!evex-byte3->v-prime$inline v-prime x)
                  (!evex-byte3->v-prime$inline v-prime-equiv x)))
  :rule-classes :congruence)

Theorem: !evex-byte3->v-prime$inline-of-evex-byte3-fix-x

(defthm !evex-byte3->v-prime$inline-of-evex-byte3-fix-x
  (equal (!evex-byte3->v-prime$inline v-prime (evex-byte3-fix x))
         (!evex-byte3->v-prime$inline v-prime x)))

Theorem: !evex-byte3->v-prime$inline-evex-byte3-equiv-congruence-on-x

(defthm !evex-byte3->v-prime$inline-evex-byte3-equiv-congruence-on-x
  (implies (evex-byte3-equiv x x-equiv)
           (equal (!evex-byte3->v-prime$inline v-prime x)
                  (!evex-byte3->v-prime$inline v-prime x-equiv)))
  :rule-classes :congruence)

Theorem: !evex-byte3->v-prime-is-evex-byte3

(defthm !evex-byte3->v-prime-is-evex-byte3
  (equal (!evex-byte3->v-prime v-prime x)
         (change-evex-byte3 x :v-prime v-prime)))

Theorem: evex-byte3->v-prime-of-!evex-byte3->v-prime

(defthm evex-byte3->v-prime-of-!evex-byte3->v-prime
  (b* ((?new-x (!evex-byte3->v-prime$inline v-prime x)))
    (equal (evex-byte3->v-prime new-x)
           (bfix v-prime))))

Theorem: !evex-byte3->v-prime-equiv-under-mask

(defthm !evex-byte3->v-prime-equiv-under-mask
  (b* ((?new-x (!evex-byte3->v-prime$inline v-prime x)))
    (evex-byte3-equiv-under-mask new-x x -9)))

Function: !evex-byte3->b$inline

(defun !evex-byte3->b$inline (b x)
 (declare (xargs :guard (and (bitp b) (evex-byte3-p x))))
 (mbe :logic
      (b* ((b (mbe :logic (bfix b) :exec b))
           (x (evex-byte3-fix x)))
        (part-install b x :width 1 :low 4))
      :exec (the (unsigned-byte 8)
                 (logior (the (unsigned-byte 8)
                              (logand (the (unsigned-byte 8) x)
                                      (the (signed-byte 6) -17)))
                         (the (unsigned-byte 5)
                              (ash (the (unsigned-byte 1) b) 4))))))

Theorem: evex-byte3-p-of-!evex-byte3->b

(defthm evex-byte3-p-of-!evex-byte3->b
  (b* ((new-x (!evex-byte3->b$inline b x)))
    (evex-byte3-p new-x))
  :rule-classes :rewrite)

Theorem: !evex-byte3->b$inline-of-bfix-b

(defthm !evex-byte3->b$inline-of-bfix-b
  (equal (!evex-byte3->b$inline (bfix b) x)
         (!evex-byte3->b$inline b x)))

Theorem: !evex-byte3->b$inline-bit-equiv-congruence-on-b

(defthm !evex-byte3->b$inline-bit-equiv-congruence-on-b
  (implies (bit-equiv b b-equiv)
           (equal (!evex-byte3->b$inline b x)
                  (!evex-byte3->b$inline b-equiv x)))
  :rule-classes :congruence)

Theorem: !evex-byte3->b$inline-of-evex-byte3-fix-x

(defthm !evex-byte3->b$inline-of-evex-byte3-fix-x
  (equal (!evex-byte3->b$inline b (evex-byte3-fix x))
         (!evex-byte3->b$inline b x)))

Theorem: !evex-byte3->b$inline-evex-byte3-equiv-congruence-on-x

(defthm !evex-byte3->b$inline-evex-byte3-equiv-congruence-on-x
  (implies (evex-byte3-equiv x x-equiv)
           (equal (!evex-byte3->b$inline b x)
                  (!evex-byte3->b$inline b x-equiv)))
  :rule-classes :congruence)

Theorem: !evex-byte3->b-is-evex-byte3

(defthm !evex-byte3->b-is-evex-byte3
  (equal (!evex-byte3->b b x)
         (change-evex-byte3 x :b b)))

Theorem: evex-byte3->b-of-!evex-byte3->b

(defthm evex-byte3->b-of-!evex-byte3->b
  (b* ((?new-x (!evex-byte3->b$inline b x)))
    (equal (evex-byte3->b new-x) (bfix b))))

Theorem: !evex-byte3->b-equiv-under-mask

(defthm !evex-byte3->b-equiv-under-mask
  (b* ((?new-x (!evex-byte3->b$inline b x)))
    (evex-byte3-equiv-under-mask new-x x -17)))

Function: !evex-byte3->vl/rc$inline

(defun !evex-byte3->vl/rc$inline (vl/rc x)
  (declare (xargs :guard (and (2bits-p vl/rc) (evex-byte3-p x))))
  (mbe :logic
       (b* ((vl/rc (mbe :logic (2bits-fix vl/rc)
                        :exec vl/rc))
            (x (evex-byte3-fix x)))
         (part-install vl/rc x :width 2 :low 5))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 8) -97)))
                          (the (unsigned-byte 7)
                               (ash (the (unsigned-byte 2) vl/rc)
                                    5))))))

Theorem: evex-byte3-p-of-!evex-byte3->vl/rc

(defthm evex-byte3-p-of-!evex-byte3->vl/rc
  (b* ((new-x (!evex-byte3->vl/rc$inline vl/rc x)))
    (evex-byte3-p new-x))
  :rule-classes :rewrite)

Theorem: !evex-byte3->vl/rc$inline-of-2bits-fix-vl/rc

(defthm !evex-byte3->vl/rc$inline-of-2bits-fix-vl/rc
  (equal (!evex-byte3->vl/rc$inline (2bits-fix vl/rc)
                                    x)
         (!evex-byte3->vl/rc$inline vl/rc x)))

Theorem: !evex-byte3->vl/rc$inline-2bits-equiv-congruence-on-vl/rc

(defthm !evex-byte3->vl/rc$inline-2bits-equiv-congruence-on-vl/rc
  (implies (2bits-equiv vl/rc vl/rc-equiv)
           (equal (!evex-byte3->vl/rc$inline vl/rc x)
                  (!evex-byte3->vl/rc$inline vl/rc-equiv x)))
  :rule-classes :congruence)

Theorem: !evex-byte3->vl/rc$inline-of-evex-byte3-fix-x

(defthm !evex-byte3->vl/rc$inline-of-evex-byte3-fix-x
  (equal (!evex-byte3->vl/rc$inline vl/rc (evex-byte3-fix x))
         (!evex-byte3->vl/rc$inline vl/rc x)))

Theorem: !evex-byte3->vl/rc$inline-evex-byte3-equiv-congruence-on-x

(defthm !evex-byte3->vl/rc$inline-evex-byte3-equiv-congruence-on-x
  (implies (evex-byte3-equiv x x-equiv)
           (equal (!evex-byte3->vl/rc$inline vl/rc x)
                  (!evex-byte3->vl/rc$inline vl/rc x-equiv)))
  :rule-classes :congruence)

Theorem: !evex-byte3->vl/rc-is-evex-byte3

(defthm !evex-byte3->vl/rc-is-evex-byte3
  (equal (!evex-byte3->vl/rc vl/rc x)
         (change-evex-byte3 x :vl/rc vl/rc)))

Theorem: evex-byte3->vl/rc-of-!evex-byte3->vl/rc

(defthm evex-byte3->vl/rc-of-!evex-byte3->vl/rc
  (b* ((?new-x (!evex-byte3->vl/rc$inline vl/rc x)))
    (equal (evex-byte3->vl/rc new-x)
           (2bits-fix vl/rc))))

Theorem: !evex-byte3->vl/rc-equiv-under-mask

(defthm !evex-byte3->vl/rc-equiv-under-mask
  (b* ((?new-x (!evex-byte3->vl/rc$inline vl/rc x)))
    (evex-byte3-equiv-under-mask new-x x -97)))

Function: !evex-byte3->z$inline

(defun !evex-byte3->z$inline (z x)
 (declare (xargs :guard (and (bitp z) (evex-byte3-p x))))
 (mbe :logic
      (b* ((z (mbe :logic (bfix z) :exec z))
           (x (evex-byte3-fix x)))
        (part-install z 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) z) 7))))))

Theorem: evex-byte3-p-of-!evex-byte3->z

(defthm evex-byte3-p-of-!evex-byte3->z
  (b* ((new-x (!evex-byte3->z$inline z x)))
    (evex-byte3-p new-x))
  :rule-classes :rewrite)

Theorem: !evex-byte3->z$inline-of-bfix-z

(defthm !evex-byte3->z$inline-of-bfix-z
  (equal (!evex-byte3->z$inline (bfix z) x)
         (!evex-byte3->z$inline z x)))

Theorem: !evex-byte3->z$inline-bit-equiv-congruence-on-z

(defthm !evex-byte3->z$inline-bit-equiv-congruence-on-z
  (implies (bit-equiv z z-equiv)
           (equal (!evex-byte3->z$inline z x)
                  (!evex-byte3->z$inline z-equiv x)))
  :rule-classes :congruence)

Theorem: !evex-byte3->z$inline-of-evex-byte3-fix-x

(defthm !evex-byte3->z$inline-of-evex-byte3-fix-x
  (equal (!evex-byte3->z$inline z (evex-byte3-fix x))
         (!evex-byte3->z$inline z x)))

Theorem: !evex-byte3->z$inline-evex-byte3-equiv-congruence-on-x

(defthm !evex-byte3->z$inline-evex-byte3-equiv-congruence-on-x
  (implies (evex-byte3-equiv x x-equiv)
           (equal (!evex-byte3->z$inline z x)
                  (!evex-byte3->z$inline z x-equiv)))
  :rule-classes :congruence)

Theorem: !evex-byte3->z-is-evex-byte3

(defthm !evex-byte3->z-is-evex-byte3
  (equal (!evex-byte3->z z x)
         (change-evex-byte3 x :z z)))

Theorem: evex-byte3->z-of-!evex-byte3->z

(defthm evex-byte3->z-of-!evex-byte3->z
  (b* ((?new-x (!evex-byte3->z$inline z x)))
    (equal (evex-byte3->z new-x) (bfix z))))

Theorem: !evex-byte3->z-equiv-under-mask

(defthm !evex-byte3->z-equiv-under-mask
  (b* ((?new-x (!evex-byte3->z$inline z x)))
    (evex-byte3-equiv-under-mask new-x x 127)))

Function: evex-byte3-debug$inline

(defun evex-byte3-debug$inline (x)
  (declare (xargs :guard (evex-byte3-p x)))
  (b* (((evex-byte3 x)))
    (cons (cons 'aaa x.aaa)
          (cons (cons 'v-prime x.v-prime)
                (cons (cons 'b x.b)
                      (cons (cons 'vl/rc x.vl/rc)
                            (cons (cons 'z x.z) nil)))))))

Function: evex->aaa$inline

(defun evex->aaa$inline (evex-prefixes)
  (declare (xargs :guard (evex-prefixes-p evex-prefixes)))
  (evex-byte3->aaa (evex-prefixes->byte3 evex-prefixes)))

Theorem: return-type-of-evex->aaa

(defthm return-type-of-evex->aaa
  (implies (and (evex-prefixes-p$inline evex-prefixes))
           (b* ((aaa (evex->aaa$inline evex-prefixes)))
             (unsigned-byte-p 3 aaa)))
  :rule-classes :rewrite)

Function: evex->z$inline

(defun evex->z$inline (evex-prefixes)
  (declare (xargs :guard (evex-prefixes-p evex-prefixes)))
  (evex-byte3->z (evex-prefixes->byte3 evex-prefixes)))

Theorem: return-type-of-evex->z

(defthm return-type-of-evex->z
  (implies (and (evex-prefixes-p$inline evex-prefixes))
           (b* ((z (evex->z$inline evex-prefixes)))
             (unsigned-byte-p 1 z)))
  :rule-classes :rewrite)

Function: evex->vvvv$inline

(defun evex->vvvv$inline (evex-prefixes)
  (declare (xargs :guard (evex-prefixes-p evex-prefixes)))
  (evex-byte2->vvvv (evex-prefixes->byte2 evex-prefixes)))

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

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

Function: evex->v-prime$inline

(defun evex->v-prime$inline (evex-prefixes)
  (declare (xargs :guard (evex-prefixes-p evex-prefixes)))
  (evex-byte3->v-prime (evex-prefixes->byte3 evex-prefixes)))

Theorem: return-type-of-evex->v-prime

(defthm return-type-of-evex->v-prime
  (implies (and (evex-prefixes-p$inline evex-prefixes))
           (b* ((v-prime (evex->v-prime$inline evex-prefixes)))
             (unsigned-byte-p 1 v-prime)))
  :rule-classes :rewrite)

Function: evex->vl/rc$inline

(defun evex->vl/rc$inline (evex-prefixes)
  (declare (xargs :guard (evex-prefixes-p evex-prefixes)))
  (evex-byte3->vl/rc (evex-prefixes->byte3 evex-prefixes)))

Theorem: return-type-of-evex->vl/rc

(defthm return-type-of-evex->vl/rc
  (implies (and (evex-prefixes-p$inline evex-prefixes))
           (b* ((vl/rc (evex->vl/rc$inline evex-prefixes)))
             (unsigned-byte-p 2 vl/rc)))
  :rule-classes :rewrite)

Function: evex->pp$inline

(defun evex->pp$inline (evex-prefixes)
  (declare (xargs :guard (evex-prefixes-p evex-prefixes)))
  (evex-byte2->pp (evex-prefixes->byte2 evex-prefixes)))

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

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

Function: evex->w$inline

(defun evex->w$inline (evex-prefixes)
  (declare (xargs :guard (evex-prefixes-p evex-prefixes)))
  (evex-byte2->w (evex-prefixes->byte2 evex-prefixes)))

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

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