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Cr4bits

!cr4bits->pae

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

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

Definitions and Theorems

Function: !cr4bits->pae$inline

(defun !cr4bits->pae$inline (pae x)
 (declare (xargs :guard (and (bitp pae) (cr4bits-p x))))
 (mbe
    :logic
    (b* ((pae (mbe :logic (bfix pae) :exec pae))
         (x (cr4bits-fix x)))
      (part-install pae x :width 1 :low 5))
    :exec (the (unsigned-byte 26)
               (logior (the (unsigned-byte 26)
                            (logand (the (unsigned-byte 26) x)
                                    (the (signed-byte 7) -33)))
                       (the (unsigned-byte 6)
                            (ash (the (unsigned-byte 1) pae) 5))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->pae-is-cr4bits

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

Theorem: cr4bits->pae-of-!cr4bits->pae

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

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

(defthm !cr4bits->pae-equiv-under-mask
  (b* ((?new-x (!cr4bits->pae$inline pae x)))
    (cr4bits-equiv-under-mask new-x x -33)))