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Evex-byte1

!evex-byte1->x

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

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

Definitions and Theorems

Function: !evex-byte1->x$inline

(defun !evex-byte1->x$inline (x byte1)
 (declare (xargs :guard (and (bitp x) (evex-byte1-p byte1))))
 (mbe :logic
      (b* ((x (mbe :logic (bfix x) :exec x))
           (byte1 (evex-byte1-fix byte1)))
        (part-install x byte1 :width 1 :low 6))
      :exec (the (unsigned-byte 8)
                 (logior (the (unsigned-byte 8)
                              (logand (the (unsigned-byte 8) byte1)
                                      (the (signed-byte 8) -65)))
                         (the (unsigned-byte 7)
                              (ash (the (unsigned-byte 1) x) 6))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !evex-byte1->x-equiv-under-mask
  (b* ((?new-byte1 (!evex-byte1->x$inline x byte1)))
    (evex-byte1-equiv-under-mask new-byte1 byte1 -65)))