		Search-engine friendly clone of the ACL2 documentation.

Vex3-byte1

!vex3-byte1->x

Update the |ACL2|::|X| field of a vex3-byte1 bit structure.

Signature
(!vex3-byte1->x x vex3byte1) → new-vex3byte1
Arguments: x — Guard (bitp x).; vex3byte1 — Guard (vex3-byte1-p vex3byte1).
Returns: new-vex3byte1 — Type (vex3-byte1-p new-vex3byte1).

Definitions and Theorems

Function: !vex3-byte1->x$inline

(defun !vex3-byte1->x$inline (x vex3byte1)
 (declare (xargs :guard (and (bitp x)
                             (vex3-byte1-p vex3byte1))))
 (mbe
   :logic
   (b* ((x (mbe :logic (bfix x) :exec x))
        (vex3byte1 (vex3-byte1-fix vex3byte1)))
     (part-install x vex3byte1
                   :width 1
                   :low 6))
   :exec (the (unsigned-byte 8)
              (logior (the (unsigned-byte 8)
                           (logand (the (unsigned-byte 8) vex3byte1)
                                   (the (signed-byte 8) -65)))
                      (the (unsigned-byte 7)
                           (ash (the (unsigned-byte 1) x) 6))))))

Theorem: vex3-byte1-p-of-!vex3-byte1->x

(defthm vex3-byte1-p-of-!vex3-byte1->x
  (b* ((new-vex3byte1 (!vex3-byte1->x$inline x vex3byte1)))
    (vex3-byte1-p new-vex3byte1))
  :rule-classes :rewrite)

Theorem: !vex3-byte1->x$inline-of-bfix-x

(defthm !vex3-byte1->x$inline-of-bfix-x
  (equal (!vex3-byte1->x$inline (bfix x)
                                vex3byte1)
         (!vex3-byte1->x$inline x vex3byte1)))

Theorem: !vex3-byte1->x$inline-bit-equiv-congruence-on-x

(defthm !vex3-byte1->x$inline-bit-equiv-congruence-on-x
  (implies (bit-equiv x x-equiv)
           (equal (!vex3-byte1->x$inline x vex3byte1)
                  (!vex3-byte1->x$inline x-equiv vex3byte1)))
  :rule-classes :congruence)

Theorem: !vex3-byte1->x$inline-of-vex3-byte1-fix-vex3byte1

(defthm !vex3-byte1->x$inline-of-vex3-byte1-fix-vex3byte1
  (equal (!vex3-byte1->x$inline x (vex3-byte1-fix vex3byte1))
         (!vex3-byte1->x$inline x vex3byte1)))

Theorem: !vex3-byte1->x$inline-vex3-byte1-equiv-congruence-on-vex3byte1

(defthm
     !vex3-byte1->x$inline-vex3-byte1-equiv-congruence-on-vex3byte1
  (implies (vex3-byte1-equiv vex3byte1 vex3byte1-equiv)
           (equal (!vex3-byte1->x$inline x vex3byte1)
                  (!vex3-byte1->x$inline x vex3byte1-equiv)))
  :rule-classes :congruence)

Theorem: !vex3-byte1->x-is-vex3-byte1

(defthm !vex3-byte1->x-is-vex3-byte1
  (equal (!vex3-byte1->x x vex3byte1)
         (change-vex3-byte1 vex3byte1 :x x)))

Theorem: vex3-byte1->x-of-!vex3-byte1->x

(defthm vex3-byte1->x-of-!vex3-byte1->x
  (b* ((?new-vex3byte1 (!vex3-byte1->x$inline x vex3byte1)))
    (equal (vex3-byte1->x new-vex3byte1)
           (bfix x))))

Theorem: !vex3-byte1->x-equiv-under-mask

(defthm !vex3-byte1->x-equiv-under-mask
  (b* ((?new-vex3byte1 (!vex3-byte1->x$inline x vex3byte1)))
    (vex3-byte1-equiv-under-mask new-vex3byte1 vex3byte1 -65)))