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Vex3-byte1

!vex3-byte1->b

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

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

Definitions and Theorems

Function: !vex3-byte1->b$inline

(defun !vex3-byte1->b$inline (b vex3byte1)
 (declare (xargs :guard (and (bitp b)
                             (vex3-byte1-p vex3byte1))))
 (mbe
   :logic
   (b* ((b (mbe :logic (bfix b) :exec b))
        (vex3byte1 (vex3-byte1-fix vex3byte1)))
     (part-install b vex3byte1
                   :width 1
                   :low 5))
   :exec (the (unsigned-byte 8)
              (logior (the (unsigned-byte 8)
                           (logand (the (unsigned-byte 8) vex3byte1)
                                   (the (signed-byte 7) -33)))
                      (the (unsigned-byte 6)
                           (ash (the (unsigned-byte 1) b) 5))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !vex3-byte1->b-equiv-under-mask
  (b* ((?new-vex3byte1 (!vex3-byte1->b$inline b vex3byte1)))
    (vex3-byte1-equiv-under-mask new-vex3byte1 vex3byte1 -33)))