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Evex-byte3

!evex-byte3->aaa

Update the |X86ISA|::|AAA| field of a evex-byte3 bit structure.

Signature
(!evex-byte3->aaa aaa x) → new-x
Arguments: aaa — Guard (3bits-p aaa).; x — Guard (evex-byte3-p x).
Returns: new-x — Type (evex-byte3-p new-x).

Definitions and Theorems

Function: !evex-byte3->aaa$inline

(defun !evex-byte3->aaa$inline (aaa x)
  (declare (xargs :guard (and (3bits-p aaa) (evex-byte3-p x))))
  (mbe :logic
       (b* ((aaa (mbe :logic (3bits-fix aaa) :exec aaa))
            (x (evex-byte3-fix x)))
         (part-install aaa x :width 3 :low 0))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 4) -8)))
                          (the (unsigned-byte 3) aaa)))))

Theorem: evex-byte3-p-of-!evex-byte3->aaa

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

Theorem: !evex-byte3->aaa$inline-of-3bits-fix-aaa

(defthm !evex-byte3->aaa$inline-of-3bits-fix-aaa
  (equal (!evex-byte3->aaa$inline (3bits-fix aaa)
                                  x)
         (!evex-byte3->aaa$inline aaa x)))

Theorem: !evex-byte3->aaa$inline-3bits-equiv-congruence-on-aaa

(defthm !evex-byte3->aaa$inline-3bits-equiv-congruence-on-aaa
  (implies (3bits-equiv aaa aaa-equiv)
           (equal (!evex-byte3->aaa$inline aaa x)
                  (!evex-byte3->aaa$inline aaa-equiv x)))
  :rule-classes :congruence)

Theorem: !evex-byte3->aaa$inline-of-evex-byte3-fix-x

(defthm !evex-byte3->aaa$inline-of-evex-byte3-fix-x
  (equal (!evex-byte3->aaa$inline aaa (evex-byte3-fix x))
         (!evex-byte3->aaa$inline aaa x)))

Theorem: !evex-byte3->aaa$inline-evex-byte3-equiv-congruence-on-x

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

Theorem: !evex-byte3->aaa-is-evex-byte3

(defthm !evex-byte3->aaa-is-evex-byte3
  (equal (!evex-byte3->aaa aaa x)
         (change-evex-byte3 x :aaa aaa)))

Theorem: evex-byte3->aaa-of-!evex-byte3->aaa

(defthm evex-byte3->aaa-of-!evex-byte3->aaa
  (b* ((?new-x (!evex-byte3->aaa$inline aaa x)))
    (equal (evex-byte3->aaa new-x)
           (3bits-fix aaa))))

Theorem: !evex-byte3->aaa-equiv-under-mask

(defthm !evex-byte3->aaa-equiv-under-mask
  (b* ((?new-x (!evex-byte3->aaa$inline aaa x)))
    (evex-byte3-equiv-under-mask new-x x -8)))