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Ia32e-pml4ebits

Ia32e-pml4ebits->xd

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

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

Definitions and Theorems

Function: ia32e-pml4ebits->xd$inline

(defun ia32e-pml4ebits->xd$inline (x)
  (declare (xargs :guard (ia32e-pml4ebits-p x)))
  (mbe :logic
       (let ((x (ia32e-pml4ebits-fix x)))
         (part-select x :low 63 :width 1))
       :exec (the (unsigned-byte 1)
                  (logand (the (unsigned-byte 1) 1)
                          (the (unsigned-byte 1)
                               (ash (the (unsigned-byte 64) x)
                                    -63))))))

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

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

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 (ia32e-pml4ebits-fix x))
         (ia32e-pml4ebits->xd$inline 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 x)
                  (ia32e-pml4ebits->xd$inline x-equiv)))
  :rule-classes :congruence)

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

(defthm ia32e-pml4ebits->xd-of-ia32e-pml4ebits
  (equal (ia32e-pml4ebits->xd
              (ia32e-pml4ebits p r/w u/s
                               pwt pcd a res1 ps res2 pdpt res3 xd))
         (bfix xd)))

Theorem: ia32e-pml4ebits->xd-of-write-with-mask

(defthm ia32e-pml4ebits->xd-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x ia32e-pml4ebits-equiv-under-mask)
                (ia32e-pml4ebits-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask)
                               9223372036854775808)
                       0))
           (equal (ia32e-pml4ebits->xd x)
                  (ia32e-pml4ebits->xd y))))