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Vex3-byte2

Vex3-byte2->pp

Access the |X86ISA|::|PP| field of a vex3-byte2 bit structure.

Signature
(vex3-byte2->pp x) → pp
Arguments: x — Guard (vex3-byte2-p x).
Returns: pp — Type (2bits-p pp).

Definitions and Theorems

Function: vex3-byte2->pp$inline

(defun vex3-byte2->pp$inline (x)
  (declare (xargs :guard (vex3-byte2-p x)))
  (mbe :logic
       (let ((x (vex3-byte2-fix x)))
         (part-select x :low 0 :width 2))
       :exec (the (unsigned-byte 2)
                  (logand (the (unsigned-byte 2) 3)
                          (the (unsigned-byte 8) x)))))

Theorem: 2bits-p-of-vex3-byte2->pp

(defthm 2bits-p-of-vex3-byte2->pp
  (b* ((pp (vex3-byte2->pp$inline x)))
    (2bits-p pp))
  :rule-classes :rewrite)

Theorem: vex3-byte2->pp$inline-of-vex3-byte2-fix-x

(defthm vex3-byte2->pp$inline-of-vex3-byte2-fix-x
  (equal (vex3-byte2->pp$inline (vex3-byte2-fix x))
         (vex3-byte2->pp$inline x)))

Theorem: vex3-byte2->pp$inline-vex3-byte2-equiv-congruence-on-x

(defthm vex3-byte2->pp$inline-vex3-byte2-equiv-congruence-on-x
  (implies (vex3-byte2-equiv x x-equiv)
           (equal (vex3-byte2->pp$inline x)
                  (vex3-byte2->pp$inline x-equiv)))
  :rule-classes :congruence)

Theorem: vex3-byte2->pp-of-vex3-byte2

(defthm vex3-byte2->pp-of-vex3-byte2
  (equal (vex3-byte2->pp (vex3-byte2 pp l vvvv w))
         (2bits-fix pp)))

Theorem: vex3-byte2->pp-of-write-with-mask

(defthm vex3-byte2->pp-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x vex3-byte2-equiv-under-mask)
                (vex3-byte2-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 3) 0))
           (equal (vex3-byte2->pp x)
                  (vex3-byte2->pp y))))