		Search-engine friendly clone of the ACL2 documentation.

Ia32e-page-tablesbits

!ia32e-page-tablesbits->d

Update the |ACL2|::|D| field of a ia32e-page-tablesbits bit structure.

Signature
(!ia32e-page-tablesbits->d d x) → new-x
Arguments: d — Guard (bitp d).; x — Guard (ia32e-page-tablesbits-p x).
Returns: new-x — Type (ia32e-page-tablesbits-p new-x).

Definitions and Theorems

Function: !ia32e-page-tablesbits->d$inline

(defun !ia32e-page-tablesbits->d$inline (d x)
 (declare (xargs :guard (and (bitp d)
                             (ia32e-page-tablesbits-p x))))
 (mbe :logic
      (b* ((d (mbe :logic (bfix d) :exec d))
           (x (ia32e-page-tablesbits-fix x)))
        (part-install d x :width 1 :low 6))
      :exec (the (unsigned-byte 64)
                 (logior (the (unsigned-byte 64)
                              (logand (the (unsigned-byte 64) x)
                                      (the (signed-byte 8) -65)))
                         (the (unsigned-byte 7)
                              (ash (the (unsigned-byte 1) d) 6))))))

Theorem: ia32e-page-tablesbits-p-of-!ia32e-page-tablesbits->d

(defthm ia32e-page-tablesbits-p-of-!ia32e-page-tablesbits->d
  (b* ((new-x (!ia32e-page-tablesbits->d$inline d x)))
    (ia32e-page-tablesbits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32e-page-tablesbits->d$inline-of-bfix-d

(defthm !ia32e-page-tablesbits->d$inline-of-bfix-d
  (equal (!ia32e-page-tablesbits->d$inline (bfix d)
                                           x)
         (!ia32e-page-tablesbits->d$inline d x)))

Theorem: !ia32e-page-tablesbits->d$inline-bit-equiv-congruence-on-d

(defthm !ia32e-page-tablesbits->d$inline-bit-equiv-congruence-on-d
  (implies (bit-equiv d d-equiv)
           (equal (!ia32e-page-tablesbits->d$inline d x)
                  (!ia32e-page-tablesbits->d$inline d-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32e-page-tablesbits->d$inline-of-ia32e-page-tablesbits-fix-x

(defthm
    !ia32e-page-tablesbits->d$inline-of-ia32e-page-tablesbits-fix-x
 (equal
  (!ia32e-page-tablesbits->d$inline d (ia32e-page-tablesbits-fix x))
  (!ia32e-page-tablesbits->d$inline d x)))

Theorem: !ia32e-page-tablesbits->d$inline-ia32e-page-tablesbits-equiv-congruence-on-x

(defthm
 !ia32e-page-tablesbits->d$inline-ia32e-page-tablesbits-equiv-congruence-on-x
 (implies (ia32e-page-tablesbits-equiv x x-equiv)
          (equal (!ia32e-page-tablesbits->d$inline d x)
                 (!ia32e-page-tablesbits->d$inline d x-equiv)))
 :rule-classes :congruence)

Theorem: !ia32e-page-tablesbits->d-is-ia32e-page-tablesbits

(defthm !ia32e-page-tablesbits->d-is-ia32e-page-tablesbits
  (equal (!ia32e-page-tablesbits->d d x)
         (change-ia32e-page-tablesbits x :d d)))

Theorem: ia32e-page-tablesbits->d-of-!ia32e-page-tablesbits->d

(defthm ia32e-page-tablesbits->d-of-!ia32e-page-tablesbits->d
  (b* ((?new-x (!ia32e-page-tablesbits->d$inline d x)))
    (equal (ia32e-page-tablesbits->d new-x)
           (bfix d))))

Theorem: !ia32e-page-tablesbits->d-equiv-under-mask

(defthm !ia32e-page-tablesbits->d-equiv-under-mask
  (b* ((?new-x (!ia32e-page-tablesbits->d$inline d x)))
    (ia32e-page-tablesbits-equiv-under-mask new-x x -65)))