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Vex3-byte2

!vex3-byte2->pp

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

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

Definitions and Theorems

Function: !vex3-byte2->pp$inline

(defun !vex3-byte2->pp$inline (pp x)
  (declare (xargs :guard (and (2bits-p pp) (vex3-byte2-p x))))
  (mbe :logic
       (b* ((pp (mbe :logic (2bits-fix pp) :exec pp))
            (x (vex3-byte2-fix x)))
         (part-install pp x :width 2 :low 0))
       :exec (the (unsigned-byte 8)
                  (logior (the (unsigned-byte 8)
                               (logand (the (unsigned-byte 8) x)
                                       (the (signed-byte 3) -4)))
                          (the (unsigned-byte 2) pp)))))

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

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

Theorem: !vex3-byte2->pp$inline-of-2bits-fix-pp

(defthm !vex3-byte2->pp$inline-of-2bits-fix-pp
  (equal (!vex3-byte2->pp$inline (2bits-fix pp)
                                 x)
         (!vex3-byte2->pp$inline pp x)))

Theorem: !vex3-byte2->pp$inline-2bits-equiv-congruence-on-pp

(defthm !vex3-byte2->pp$inline-2bits-equiv-congruence-on-pp
  (implies (2bits-equiv pp pp-equiv)
           (equal (!vex3-byte2->pp$inline pp x)
                  (!vex3-byte2->pp$inline pp-equiv x)))
  :rule-classes :congruence)

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 pp (vex3-byte2-fix x))
         (!vex3-byte2->pp$inline pp 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 pp x)
                  (!vex3-byte2->pp$inline pp x-equiv)))
  :rule-classes :congruence)

Theorem: !vex3-byte2->pp-is-vex3-byte2

(defthm !vex3-byte2->pp-is-vex3-byte2
  (equal (!vex3-byte2->pp pp x)
         (change-vex3-byte2 x :pp pp)))

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

(defthm vex3-byte2->pp-of-!vex3-byte2->pp
  (b* ((?new-x (!vex3-byte2->pp$inline pp x)))
    (equal (vex3-byte2->pp new-x)
           (2bits-fix pp))))

Theorem: !vex3-byte2->pp-equiv-under-mask

(defthm !vex3-byte2->pp-equiv-under-mask
  (b* ((?new-x (!vex3-byte2->pp$inline pp x)))
    (vex3-byte2-equiv-under-mask new-x x -4)))