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Cr4bits

!cr4bits->mce

Update the |X86ISA|::|MCE| field of a cr4bits bit structure.

Signature
(!cr4bits->mce mce x) → new-x
Arguments: mce — Guard (bitp mce).; x — Guard (cr4bits-p x).
Returns: new-x — Type (cr4bits-p new-x).

Definitions and Theorems

Function: !cr4bits->mce$inline

(defun !cr4bits->mce$inline (mce x)
 (declare (xargs :guard (and (bitp mce) (cr4bits-p x))))
 (mbe
    :logic
    (b* ((mce (mbe :logic (bfix mce) :exec mce))
         (x (cr4bits-fix x)))
      (part-install mce x :width 1 :low 6))
    :exec (the (unsigned-byte 26)
               (logior (the (unsigned-byte 26)
                            (logand (the (unsigned-byte 26) x)
                                    (the (signed-byte 8) -65)))
                       (the (unsigned-byte 7)
                            (ash (the (unsigned-byte 1) mce) 6))))))

Theorem: cr4bits-p-of-!cr4bits->mce

(defthm cr4bits-p-of-!cr4bits->mce
  (b* ((new-x (!cr4bits->mce$inline mce x)))
    (cr4bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr4bits->mce$inline-of-bfix-mce

(defthm !cr4bits->mce$inline-of-bfix-mce
  (equal (!cr4bits->mce$inline (bfix mce) x)
         (!cr4bits->mce$inline mce x)))

Theorem: !cr4bits->mce$inline-bit-equiv-congruence-on-mce

(defthm !cr4bits->mce$inline-bit-equiv-congruence-on-mce
  (implies (bit-equiv mce mce-equiv)
           (equal (!cr4bits->mce$inline mce x)
                  (!cr4bits->mce$inline mce-equiv x)))
  :rule-classes :congruence)

Theorem: !cr4bits->mce$inline-of-cr4bits-fix-x

(defthm !cr4bits->mce$inline-of-cr4bits-fix-x
  (equal (!cr4bits->mce$inline mce (cr4bits-fix x))
         (!cr4bits->mce$inline mce x)))

Theorem: !cr4bits->mce$inline-cr4bits-equiv-congruence-on-x

(defthm !cr4bits->mce$inline-cr4bits-equiv-congruence-on-x
  (implies (cr4bits-equiv x x-equiv)
           (equal (!cr4bits->mce$inline mce x)
                  (!cr4bits->mce$inline mce x-equiv)))
  :rule-classes :congruence)

Theorem: !cr4bits->mce-is-cr4bits

(defthm !cr4bits->mce-is-cr4bits
  (equal (!cr4bits->mce mce x)
         (change-cr4bits x :mce mce)))

Theorem: cr4bits->mce-of-!cr4bits->mce

(defthm cr4bits->mce-of-!cr4bits->mce
  (b* ((?new-x (!cr4bits->mce$inline mce x)))
    (equal (cr4bits->mce new-x)
           (bfix mce))))

Theorem: !cr4bits->mce-equiv-under-mask

(defthm !cr4bits->mce-equiv-under-mask
  (b* ((?new-x (!cr4bits->mce$inline mce x)))
    (cr4bits-equiv-under-mask new-x x -65)))