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Cr4bits

!cr4bits->pks

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

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

Definitions and Theorems

Function: !cr4bits->pks$inline

(defun !cr4bits->pks$inline (pks x)
 (declare (xargs :guard (and (bitp pks) (cr4bits-p x))))
 (mbe
  :logic
  (b* ((pks (mbe :logic (bfix pks) :exec pks))
       (x (cr4bits-fix x)))
    (part-install pks x :width 1 :low 24))
  :exec (the (unsigned-byte 26)
             (logior (the (unsigned-byte 26)
                          (logand (the (unsigned-byte 26) x)
                                  (the (signed-byte 26) -16777217)))
                     (the (unsigned-byte 25)
                          (ash (the (unsigned-byte 1) pks)
                               24))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->pks-is-cr4bits

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

Theorem: cr4bits->pks-of-!cr4bits->pks

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

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

(defthm !cr4bits->pks-equiv-under-mask
  (b* ((?new-x (!cr4bits->pks$inline pks x)))
    (cr4bits-equiv-under-mask new-x x -16777217)))