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Evex-byte2

!evex-byte2->res

Update the |X86ISA|::|RES| field of a evex-byte2 bit structure.

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

Definitions and Theorems

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)))