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Ia32e-page-tablesbits

!ia32e-page-tablesbits->pcd

Update the |X86ISA|::|PCD| field of a ia32e-page-tablesbits bit structure.

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

Definitions and Theorems

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

(defun !ia32e-page-tablesbits->pcd$inline (pcd x)
 (declare (xargs :guard (and (bitp pcd)
                             (ia32e-page-tablesbits-p x))))
 (mbe
    :logic
    (b* ((pcd (mbe :logic (bfix pcd) :exec pcd))
         (x (ia32e-page-tablesbits-fix x)))
      (part-install pcd x :width 1 :low 4))
    :exec (the (unsigned-byte 64)
               (logior (the (unsigned-byte 64)
                            (logand (the (unsigned-byte 64) x)
                                    (the (signed-byte 6) -17)))
                       (the (unsigned-byte 5)
                            (ash (the (unsigned-byte 1) pcd) 4))))))

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(defthm !ia32e-page-tablesbits->pcd-equiv-under-mask
  (b* ((?new-x (!ia32e-page-tablesbits->pcd$inline pcd x)))
    (ia32e-page-tablesbits-equiv-under-mask new-x x -17)))