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Cr0bits

!cr0bits->cd

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

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

Definitions and Theorems

Function: !cr0bits->cd$inline

(defun !cr0bits->cd$inline (cd x)
 (declare (xargs :guard (and (bitp cd) (cr0bits-p x))))
 (mbe :logic
      (b* ((cd (mbe :logic (bfix cd) :exec cd))
           (x (cr0bits-fix x)))
        (part-install cd x :width 1 :low 30))
      :exec
      (the (unsigned-byte 32)
           (logior (the (unsigned-byte 32)
                        (logand (the (unsigned-byte 32) x)
                                (the (signed-byte 32) -1073741825)))
                   (the (unsigned-byte 31)
                        (ash (the (unsigned-byte 1) cd) 30))))))

Theorem: cr0bits-p-of-!cr0bits->cd

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

Theorem: !cr0bits->cd$inline-of-bfix-cd

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

Theorem: !cr0bits->cd$inline-bit-equiv-congruence-on-cd

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

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

(defthm !cr0bits->cd$inline-of-cr0bits-fix-x
  (equal (!cr0bits->cd$inline cd (cr0bits-fix x))
         (!cr0bits->cd$inline cd 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 cd x)
                  (!cr0bits->cd$inline cd x-equiv)))
  :rule-classes :congruence)

Theorem: !cr0bits->cd-is-cr0bits

(defthm !cr0bits->cd-is-cr0bits
  (equal (!cr0bits->cd cd x)
         (change-cr0bits x :cd cd)))

Theorem: cr0bits->cd-of-!cr0bits->cd

(defthm cr0bits->cd-of-!cr0bits->cd
  (b* ((?new-x (!cr0bits->cd$inline cd x)))
    (equal (cr0bits->cd new-x) (bfix cd))))

Theorem: !cr0bits->cd-equiv-under-mask

(defthm !cr0bits->cd-equiv-under-mask
  (b* ((?new-x (!cr0bits->cd$inline cd x)))
    (cr0bits-equiv-under-mask new-x x -1073741825)))