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Evex-byte3

!evex-byte3->z

Update the |ACL2|::|Z| field of a evex-byte3 bit structure.

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

Definitions and Theorems

Function: !evex-byte3->z$inline

(defun !evex-byte3->z$inline (z x)
 (declare (xargs :guard (and (bitp z) (evex-byte3-p x))))
 (mbe :logic
      (b* ((z (mbe :logic (bfix z) :exec z))
           (x (evex-byte3-fix x)))
        (part-install z 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) z) 7))))))

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

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

Theorem: !evex-byte3->z$inline-of-bfix-z

(defthm !evex-byte3->z$inline-of-bfix-z
  (equal (!evex-byte3->z$inline (bfix z) x)
         (!evex-byte3->z$inline z x)))

Theorem: !evex-byte3->z$inline-bit-equiv-congruence-on-z

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

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

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

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

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

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

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

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

(defthm evex-byte3->z-of-!evex-byte3->z
  (b* ((?new-x (!evex-byte3->z$inline z x)))
    (equal (evex-byte3->z new-x) (bfix z))))

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

(defthm !evex-byte3->z-equiv-under-mask
  (b* ((?new-x (!evex-byte3->z$inline z x)))
    (evex-byte3-equiv-under-mask new-x x 127)))