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Ia32_eferbits

!ia32_eferbits->nxe

Update the |X86ISA|::|NXE| field of a ia32_eferbits bit structure.

Signature
(!ia32_eferbits->nxe nxe x) → new-x
Arguments: nxe — Guard (bitp nxe).; x — Guard (ia32_eferbits-p x).
Returns: new-x — Type (ia32_eferbits-p new-x).

Definitions and Theorems

Function: !ia32_eferbits->nxe$inline

(defun !ia32_eferbits->nxe$inline (nxe x)
 (declare (xargs :guard (and (bitp nxe) (ia32_eferbits-p x))))
 (mbe :logic
      (b* ((nxe (mbe :logic (bfix nxe) :exec nxe))
           (x (ia32_eferbits-fix x)))
        (part-install nxe x :width 1 :low 11))
      :exec (the (unsigned-byte 12)
                 (logior (the (unsigned-byte 12)
                              (logand (the (unsigned-byte 12) x)
                                      (the (signed-byte 13) -2049)))
                         (the (unsigned-byte 12)
                              (ash (the (unsigned-byte 1) nxe)
                                   11))))))

Theorem: ia32_eferbits-p-of-!ia32_eferbits->nxe

(defthm ia32_eferbits-p-of-!ia32_eferbits->nxe
  (b* ((new-x (!ia32_eferbits->nxe$inline nxe x)))
    (ia32_eferbits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32_eferbits->nxe$inline-of-bfix-nxe

(defthm !ia32_eferbits->nxe$inline-of-bfix-nxe
  (equal (!ia32_eferbits->nxe$inline (bfix nxe)
                                     x)
         (!ia32_eferbits->nxe$inline nxe x)))

Theorem: !ia32_eferbits->nxe$inline-bit-equiv-congruence-on-nxe

(defthm !ia32_eferbits->nxe$inline-bit-equiv-congruence-on-nxe
  (implies (bit-equiv nxe nxe-equiv)
           (equal (!ia32_eferbits->nxe$inline nxe x)
                  (!ia32_eferbits->nxe$inline nxe-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32_eferbits->nxe$inline-of-ia32_eferbits-fix-x

(defthm !ia32_eferbits->nxe$inline-of-ia32_eferbits-fix-x
  (equal (!ia32_eferbits->nxe$inline nxe (ia32_eferbits-fix x))
         (!ia32_eferbits->nxe$inline nxe x)))

Theorem: !ia32_eferbits->nxe$inline-ia32_eferbits-equiv-congruence-on-x

(defthm
     !ia32_eferbits->nxe$inline-ia32_eferbits-equiv-congruence-on-x
  (implies (ia32_eferbits-equiv x x-equiv)
           (equal (!ia32_eferbits->nxe$inline nxe x)
                  (!ia32_eferbits->nxe$inline nxe x-equiv)))
  :rule-classes :congruence)

Theorem: !ia32_eferbits->nxe-is-ia32_eferbits

(defthm !ia32_eferbits->nxe-is-ia32_eferbits
  (equal (!ia32_eferbits->nxe nxe x)
         (change-ia32_eferbits x :nxe nxe)))

Theorem: ia32_eferbits->nxe-of-!ia32_eferbits->nxe

(defthm ia32_eferbits->nxe-of-!ia32_eferbits->nxe
  (b* ((?new-x (!ia32_eferbits->nxe$inline nxe x)))
    (equal (ia32_eferbits->nxe new-x)
           (bfix nxe))))

Theorem: !ia32_eferbits->nxe-equiv-under-mask

(defthm !ia32_eferbits->nxe-equiv-under-mask
  (b* ((?new-x (!ia32_eferbits->nxe$inline nxe x)))
    (ia32_eferbits-equiv-under-mask new-x x 2047)))