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Cr0bits

Cr0bits->cd

Access the |X86ISA|::|CD| field of a cr0bits bit structure.

Signature
(cr0bits->cd x) → cd
Arguments: x — Guard (cr0bits-p x).
Returns: cd — Type (bitp cd).

Definitions and Theorems

Function: cr0bits->cd$inline

(defun cr0bits->cd$inline (x)
  (declare (xargs :guard (cr0bits-p x)))
  (mbe :logic
       (let ((x (cr0bits-fix x)))
         (part-select x :low 30 :width 1))
       :exec (the (unsigned-byte 1)
                  (logand (the (unsigned-byte 1) 1)
                          (the (unsigned-byte 2)
                               (ash (the (unsigned-byte 32) x)
                                    -30))))))

Theorem: bitp-of-cr0bits->cd

(defthm bitp-of-cr0bits->cd
  (b* ((cd (cr0bits->cd$inline x)))
    (bitp cd))
  :rule-classes :rewrite)

Theorem: cr0bits->cd$inline-of-cr0bits-fix-x

(defthm cr0bits->cd$inline-of-cr0bits-fix-x
  (equal (cr0bits->cd$inline (cr0bits-fix x))
         (cr0bits->cd$inline x)))

Theorem: cr0bits->cd$inline-cr0bits-equiv-congruence-on-x

(defthm cr0bits->cd$inline-cr0bits-equiv-congruence-on-x
  (implies (cr0bits-equiv x x-equiv)
           (equal (cr0bits->cd$inline x)
                  (cr0bits->cd$inline x-equiv)))
  :rule-classes :congruence)

Theorem: cr0bits->cd-of-cr0bits

(defthm cr0bits->cd-of-cr0bits
 (equal
      (cr0bits->cd (cr0bits pe mp em
                            ts et ne res1 wp res2 am res3 nw cd pg))
      (bfix cd)))

Theorem: cr0bits->cd-of-write-with-mask

(defthm cr0bits->cd-of-write-with-mask
 (implies
  (and
    (fty::bitstruct-read-over-write-hyps x cr0bits-equiv-under-mask)
    (cr0bits-equiv-under-mask x y fty::mask)
    (equal (logand (lognot fty::mask) 1073741824)
           0))
  (equal (cr0bits->cd x)
         (cr0bits->cd y))))