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Evex-prefixes

!evex-prefixes->byte0

Update the |X86ISA|::|BYTE0| field of a evex-prefixes bit structure.

Signature
(!evex-prefixes->byte0 byte0 x) → new-x
Arguments: byte0 — Guard (8bits-p byte0).; x — Guard (evex-prefixes-p x).
Returns: new-x — Type (evex-prefixes-p new-x).

Definitions and Theorems

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)))