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Cr4bits

!cr4bits->kl

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

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

Definitions and Theorems

Function: !cr4bits->kl$inline

(defun !cr4bits->kl$inline (kl x)
 (declare (xargs :guard (and (bitp kl) (cr4bits-p x))))
 (mbe
    :logic
    (b* ((kl (mbe :logic (bfix kl) :exec kl))
         (x (cr4bits-fix x)))
      (part-install kl x :width 1 :low 19))
    :exec (the (unsigned-byte 26)
               (logior (the (unsigned-byte 26)
                            (logand (the (unsigned-byte 26) x)
                                    (the (signed-byte 21) -524289)))
                       (the (unsigned-byte 20)
                            (ash (the (unsigned-byte 1) kl) 19))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->kl-is-cr4bits

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

Theorem: cr4bits->kl-of-!cr4bits->kl

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

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

(defthm !cr4bits->kl-equiv-under-mask
  (b* ((?new-x (!cr4bits->kl$inline kl x)))
    (cr4bits-equiv-under-mask new-x x -524289)))