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Evex-byte1

!evex-byte1->r

Update the |ACL2|::|R| field of a evex-byte1 bit structure.

Signature
(!evex-byte1->r r byte1) → new-byte1
Arguments: r — Guard (bitp r).; byte1 — Guard (evex-byte1-p byte1).
Returns: new-byte1 — Type (evex-byte1-p new-byte1).

Definitions and Theorems

Function: !evex-byte1->r$inline

(defun !evex-byte1->r$inline (r byte1)
 (declare (xargs :guard (and (bitp r) (evex-byte1-p byte1))))
 (mbe :logic
      (b* ((r (mbe :logic (bfix r) :exec r))
           (byte1 (evex-byte1-fix byte1)))
        (part-install r byte1 :width 1 :low 7))
      :exec (the (unsigned-byte 8)
                 (logior (the (unsigned-byte 8)
                              (logand (the (unsigned-byte 8) byte1)
                                      (the (signed-byte 9) -129)))
                         (the (unsigned-byte 8)
                              (ash (the (unsigned-byte 1) r) 7))))))

Theorem: evex-byte1-p-of-!evex-byte1->r

(defthm evex-byte1-p-of-!evex-byte1->r
  (b* ((new-byte1 (!evex-byte1->r$inline r byte1)))
    (evex-byte1-p new-byte1))
  :rule-classes :rewrite)

Theorem: !evex-byte1->r$inline-of-bfix-r

(defthm !evex-byte1->r$inline-of-bfix-r
  (equal (!evex-byte1->r$inline (bfix r) byte1)
         (!evex-byte1->r$inline r byte1)))

Theorem: !evex-byte1->r$inline-bit-equiv-congruence-on-r

(defthm !evex-byte1->r$inline-bit-equiv-congruence-on-r
  (implies (bit-equiv r r-equiv)
           (equal (!evex-byte1->r$inline r byte1)
                  (!evex-byte1->r$inline r-equiv byte1)))
  :rule-classes :congruence)

Theorem: !evex-byte1->r$inline-of-evex-byte1-fix-byte1

(defthm !evex-byte1->r$inline-of-evex-byte1-fix-byte1
  (equal (!evex-byte1->r$inline r (evex-byte1-fix byte1))
         (!evex-byte1->r$inline r byte1)))

Theorem: !evex-byte1->r$inline-evex-byte1-equiv-congruence-on-byte1

(defthm !evex-byte1->r$inline-evex-byte1-equiv-congruence-on-byte1
  (implies (evex-byte1-equiv byte1 byte1-equiv)
           (equal (!evex-byte1->r$inline r byte1)
                  (!evex-byte1->r$inline r byte1-equiv)))
  :rule-classes :congruence)

Theorem: !evex-byte1->r-is-evex-byte1

(defthm !evex-byte1->r-is-evex-byte1
  (equal (!evex-byte1->r r byte1)
         (change-evex-byte1 byte1 :r r)))

Theorem: evex-byte1->r-of-!evex-byte1->r

(defthm evex-byte1->r-of-!evex-byte1->r
  (b* ((?new-byte1 (!evex-byte1->r$inline r byte1)))
    (equal (evex-byte1->r new-byte1)
           (bfix r))))

Theorem: !evex-byte1->r-equiv-under-mask

(defthm !evex-byte1->r-equiv-under-mask
  (b* ((?new-byte1 (!evex-byte1->r$inline r byte1)))
    (evex-byte1-equiv-under-mask new-byte1 byte1 127)))