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Evex-byte3

!evex-byte3->b

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

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

Definitions and Theorems

Function: !evex-byte3->b$inline

(defun !evex-byte3->b$inline (b x)
 (declare (xargs :guard (and (bitp b) (evex-byte3-p x))))
 (mbe :logic
      (b* ((b (mbe :logic (bfix b) :exec b))
           (x (evex-byte3-fix x)))
        (part-install b x :width 1 :low 4))
      :exec (the (unsigned-byte 8)
                 (logior (the (unsigned-byte 8)
                              (logand (the (unsigned-byte 8) x)
                                      (the (signed-byte 6) -17)))
                         (the (unsigned-byte 5)
                              (ash (the (unsigned-byte 1) b) 4))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !evex-byte3->b-equiv-under-mask
  (b* ((?new-x (!evex-byte3->b$inline b x)))
    (evex-byte3-equiv-under-mask new-x x -17)))