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Evex-byte3

!evex-byte3->vl/rc

Update the |X86ISA|::|VL/RC| field of a evex-byte3 bit structure.

Signature
(!evex-byte3->vl/rc vl/rc x) → new-x
Arguments: vl/rc — Guard (2bits-p vl/rc).; x — Guard (evex-byte3-p x).
Returns: new-x — Type (evex-byte3-p new-x).

Definitions and Theorems

Function: !evex-byte3->vl/rc$inline

(defun !evex-byte3->vl/rc$inline (vl/rc x)
  (declare (xargs :guard (and (2bits-p vl/rc) (evex-byte3-p x))))
  (mbe :logic
       (b* ((vl/rc (mbe :logic (2bits-fix vl/rc)
                        :exec vl/rc))
            (x (evex-byte3-fix x)))
         (part-install vl/rc x :width 2 :low 5))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 8) -97)))
                          (the (unsigned-byte 7)
                               (ash (the (unsigned-byte 2) vl/rc)
                                    5))))))

Theorem: evex-byte3-p-of-!evex-byte3->vl/rc

(defthm evex-byte3-p-of-!evex-byte3->vl/rc
  (b* ((new-x (!evex-byte3->vl/rc$inline vl/rc x)))
    (evex-byte3-p new-x))
  :rule-classes :rewrite)

Theorem: !evex-byte3->vl/rc$inline-of-2bits-fix-vl/rc

(defthm !evex-byte3->vl/rc$inline-of-2bits-fix-vl/rc
  (equal (!evex-byte3->vl/rc$inline (2bits-fix vl/rc)
                                    x)
         (!evex-byte3->vl/rc$inline vl/rc x)))

Theorem: !evex-byte3->vl/rc$inline-2bits-equiv-congruence-on-vl/rc

(defthm !evex-byte3->vl/rc$inline-2bits-equiv-congruence-on-vl/rc
  (implies (2bits-equiv vl/rc vl/rc-equiv)
           (equal (!evex-byte3->vl/rc$inline vl/rc x)
                  (!evex-byte3->vl/rc$inline vl/rc-equiv x)))
  :rule-classes :congruence)

Theorem: !evex-byte3->vl/rc$inline-of-evex-byte3-fix-x

(defthm !evex-byte3->vl/rc$inline-of-evex-byte3-fix-x
  (equal (!evex-byte3->vl/rc$inline vl/rc (evex-byte3-fix x))
         (!evex-byte3->vl/rc$inline vl/rc x)))

Theorem: !evex-byte3->vl/rc$inline-evex-byte3-equiv-congruence-on-x

(defthm !evex-byte3->vl/rc$inline-evex-byte3-equiv-congruence-on-x
  (implies (evex-byte3-equiv x x-equiv)
           (equal (!evex-byte3->vl/rc$inline vl/rc x)
                  (!evex-byte3->vl/rc$inline vl/rc x-equiv)))
  :rule-classes :congruence)

Theorem: !evex-byte3->vl/rc-is-evex-byte3

(defthm !evex-byte3->vl/rc-is-evex-byte3
  (equal (!evex-byte3->vl/rc vl/rc x)
         (change-evex-byte3 x :vl/rc vl/rc)))

Theorem: evex-byte3->vl/rc-of-!evex-byte3->vl/rc

(defthm evex-byte3->vl/rc-of-!evex-byte3->vl/rc
  (b* ((?new-x (!evex-byte3->vl/rc$inline vl/rc x)))
    (equal (evex-byte3->vl/rc new-x)
           (2bits-fix vl/rc))))

Theorem: !evex-byte3->vl/rc-equiv-under-mask

(defthm !evex-byte3->vl/rc-equiv-under-mask
  (b* ((?new-x (!evex-byte3->vl/rc$inline vl/rc x)))
    (evex-byte3-equiv-under-mask new-x x -97)))