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Vex3-byte2

!vex3-byte2->w

Update the |ACL2|::|W| field of a vex3-byte2 bit structure.

Signature
(!vex3-byte2->w w x) → new-x
Arguments: w — Guard (bitp w).; x — Guard (vex3-byte2-p x).
Returns: new-x — Type (vex3-byte2-p new-x).

Definitions and Theorems

Function: !vex3-byte2->w$inline

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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