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Ia32e-pdpte-1gb-pagebits

!ia32e-pdpte-1gb-pagebits->r/w

Update the |X86ISA|::|R/W| field of a ia32e-pdpte-1gb-pagebits bit structure.

Signature
(!ia32e-pdpte-1gb-pagebits->r/w r/w x) → new-x
Arguments: r/w — Guard (bitp r/w).; x — Guard (ia32e-pdpte-1gb-pagebits-p x).
Returns: new-x — Type (ia32e-pdpte-1gb-pagebits-p new-x).

Definitions and Theorems

Function: !ia32e-pdpte-1gb-pagebits->r/w$inline

(defun !ia32e-pdpte-1gb-pagebits->r/w$inline (r/w x)
 (declare (xargs :guard (and (bitp r/w)
                             (ia32e-pdpte-1gb-pagebits-p x))))
 (mbe
    :logic
    (b* ((r/w (mbe :logic (bfix r/w) :exec r/w))
         (x (ia32e-pdpte-1gb-pagebits-fix x)))
      (part-install r/w x :width 1 :low 1))
    :exec (the (unsigned-byte 64)
               (logior (the (unsigned-byte 64)
                            (logand (the (unsigned-byte 64) x)
                                    (the (signed-byte 3) -3)))
                       (the (unsigned-byte 2)
                            (ash (the (unsigned-byte 1) r/w) 1))))))

Theorem: ia32e-pdpte-1gb-pagebits-p-of-!ia32e-pdpte-1gb-pagebits->r/w

(defthm ia32e-pdpte-1gb-pagebits-p-of-!ia32e-pdpte-1gb-pagebits->r/w
  (b* ((new-x (!ia32e-pdpte-1gb-pagebits->r/w$inline r/w x)))
    (ia32e-pdpte-1gb-pagebits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32e-pdpte-1gb-pagebits->r/w$inline-of-bfix-r/w

(defthm !ia32e-pdpte-1gb-pagebits->r/w$inline-of-bfix-r/w
  (equal (!ia32e-pdpte-1gb-pagebits->r/w$inline (bfix r/w)
                                                x)
         (!ia32e-pdpte-1gb-pagebits->r/w$inline r/w x)))

Theorem: !ia32e-pdpte-1gb-pagebits->r/w$inline-bit-equiv-congruence-on-r/w

(defthm
  !ia32e-pdpte-1gb-pagebits->r/w$inline-bit-equiv-congruence-on-r/w
  (implies
       (bit-equiv r/w r/w-equiv)
       (equal (!ia32e-pdpte-1gb-pagebits->r/w$inline r/w x)
              (!ia32e-pdpte-1gb-pagebits->r/w$inline r/w-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32e-pdpte-1gb-pagebits->r/w$inline-of-ia32e-pdpte-1gb-pagebits-fix-x

(defthm
 !ia32e-pdpte-1gb-pagebits->r/w$inline-of-ia32e-pdpte-1gb-pagebits-fix-x
 (equal (!ia32e-pdpte-1gb-pagebits->r/w$inline
             r/w (ia32e-pdpte-1gb-pagebits-fix x))
        (!ia32e-pdpte-1gb-pagebits->r/w$inline r/w x)))

Theorem: !ia32e-pdpte-1gb-pagebits->r/w$inline-ia32e-pdpte-1gb-pagebits-equiv-congruence-on-x

(defthm
 !ia32e-pdpte-1gb-pagebits->r/w$inline-ia32e-pdpte-1gb-pagebits-equiv-congruence-on-x
 (implies
      (ia32e-pdpte-1gb-pagebits-equiv x x-equiv)
      (equal (!ia32e-pdpte-1gb-pagebits->r/w$inline r/w x)
             (!ia32e-pdpte-1gb-pagebits->r/w$inline r/w x-equiv)))
 :rule-classes :congruence)

Theorem: !ia32e-pdpte-1gb-pagebits->r/w-is-ia32e-pdpte-1gb-pagebits

(defthm !ia32e-pdpte-1gb-pagebits->r/w-is-ia32e-pdpte-1gb-pagebits
  (equal (!ia32e-pdpte-1gb-pagebits->r/w r/w x)
         (change-ia32e-pdpte-1gb-pagebits x
                                          :r/w r/w)))

Theorem: ia32e-pdpte-1gb-pagebits->r/w-of-!ia32e-pdpte-1gb-pagebits->r/w

(defthm
    ia32e-pdpte-1gb-pagebits->r/w-of-!ia32e-pdpte-1gb-pagebits->r/w
  (b* ((?new-x (!ia32e-pdpte-1gb-pagebits->r/w$inline r/w x)))
    (equal (ia32e-pdpte-1gb-pagebits->r/w new-x)
           (bfix r/w))))

Theorem: !ia32e-pdpte-1gb-pagebits->r/w-equiv-under-mask

(defthm !ia32e-pdpte-1gb-pagebits->r/w-equiv-under-mask
  (b* ((?new-x (!ia32e-pdpte-1gb-pagebits->r/w$inline r/w x)))
    (ia32e-pdpte-1gb-pagebits-equiv-under-mask new-x x -3)))