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Vex-prefixes

!vex-prefixes->byte2

Update the |X86ISA|::|BYTE2| field of a vex-prefixes bit structure.

Signature
(!vex-prefixes->byte2 byte2 x) → new-x
Arguments: byte2 — Guard (8bits-p byte2).; x — Guard (vex-prefixes-p x).
Returns: new-x — Type (vex-prefixes-p new-x).

Definitions and Theorems

Function: !vex-prefixes->byte2$inline

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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