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Vex-prefixes

!vex-prefixes->byte0

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

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

Definitions and Theorems

Function: !vex-prefixes->byte0$inline

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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