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Ia32e-pml4ebits

!ia32e-pml4ebits->xd

Update the |X86ISA|::|XD| field of a ia32e-pml4ebits bit structure.

Signature
(!ia32e-pml4ebits->xd xd x) → new-x
Arguments: xd — Guard (bitp xd).; x — Guard (ia32e-pml4ebits-p x).
Returns: new-x — Type (ia32e-pml4ebits-p new-x).

Definitions and Theorems

Function: !ia32e-pml4ebits->xd$inline

(defun !ia32e-pml4ebits->xd$inline (xd x)
 (declare (xargs :guard (and (bitp xd) (ia32e-pml4ebits-p x))))
 (mbe
    :logic
    (b* ((xd (mbe :logic (bfix xd) :exec xd))
         (x (ia32e-pml4ebits-fix x)))
      (part-install xd x :width 1 :low 63))
    :exec (the (unsigned-byte 64)
               (logior (the (unsigned-byte 64)
                            (logand (the (unsigned-byte 64) x)
                                    (the (signed-byte 65)
                                         -9223372036854775809)))
                       (the (unsigned-byte 64)
                            (ash (the (unsigned-byte 1) xd) 63))))))

Theorem: ia32e-pml4ebits-p-of-!ia32e-pml4ebits->xd

(defthm ia32e-pml4ebits-p-of-!ia32e-pml4ebits->xd
  (b* ((new-x (!ia32e-pml4ebits->xd$inline xd x)))
    (ia32e-pml4ebits-p new-x))
  :rule-classes :rewrite)

Theorem: !ia32e-pml4ebits->xd$inline-of-bfix-xd

(defthm !ia32e-pml4ebits->xd$inline-of-bfix-xd
  (equal (!ia32e-pml4ebits->xd$inline (bfix xd)
                                      x)
         (!ia32e-pml4ebits->xd$inline xd x)))

Theorem: !ia32e-pml4ebits->xd$inline-bit-equiv-congruence-on-xd

(defthm !ia32e-pml4ebits->xd$inline-bit-equiv-congruence-on-xd
  (implies (bit-equiv xd xd-equiv)
           (equal (!ia32e-pml4ebits->xd$inline xd x)
                  (!ia32e-pml4ebits->xd$inline xd-equiv x)))
  :rule-classes :congruence)

Theorem: !ia32e-pml4ebits->xd$inline-of-ia32e-pml4ebits-fix-x

(defthm !ia32e-pml4ebits->xd$inline-of-ia32e-pml4ebits-fix-x
  (equal (!ia32e-pml4ebits->xd$inline xd (ia32e-pml4ebits-fix x))
         (!ia32e-pml4ebits->xd$inline xd x)))

Theorem: !ia32e-pml4ebits->xd$inline-ia32e-pml4ebits-equiv-congruence-on-x

(defthm
  !ia32e-pml4ebits->xd$inline-ia32e-pml4ebits-equiv-congruence-on-x
  (implies (ia32e-pml4ebits-equiv x x-equiv)
           (equal (!ia32e-pml4ebits->xd$inline xd x)
                  (!ia32e-pml4ebits->xd$inline xd x-equiv)))
  :rule-classes :congruence)

Theorem: !ia32e-pml4ebits->xd-is-ia32e-pml4ebits

(defthm !ia32e-pml4ebits->xd-is-ia32e-pml4ebits
  (equal (!ia32e-pml4ebits->xd xd x)
         (change-ia32e-pml4ebits x :xd xd)))

Theorem: ia32e-pml4ebits->xd-of-!ia32e-pml4ebits->xd

(defthm ia32e-pml4ebits->xd-of-!ia32e-pml4ebits->xd
  (b* ((?new-x (!ia32e-pml4ebits->xd$inline xd x)))
    (equal (ia32e-pml4ebits->xd new-x)
           (bfix xd))))

Theorem: !ia32e-pml4ebits->xd-equiv-under-mask

(defthm !ia32e-pml4ebits->xd-equiv-under-mask
  (b* ((?new-x (!ia32e-pml4ebits->xd$inline xd x)))
    (ia32e-pml4ebits-equiv-under-mask new-x x 9223372036854775807)))