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Cr4bits

!cr4bits->pvi

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

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

Definitions and Theorems

Function: !cr4bits->pvi$inline

(defun !cr4bits->pvi$inline (pvi x)
 (declare (xargs :guard (and (bitp pvi) (cr4bits-p x))))
 (mbe
    :logic
    (b* ((pvi (mbe :logic (bfix pvi) :exec pvi))
         (x (cr4bits-fix x)))
      (part-install pvi x :width 1 :low 1))
    :exec (the (unsigned-byte 26)
               (logior (the (unsigned-byte 26)
                            (logand (the (unsigned-byte 26) x)
                                    (the (signed-byte 3) -3)))
                       (the (unsigned-byte 2)
                            (ash (the (unsigned-byte 1) pvi) 1))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->pvi-is-cr4bits

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

Theorem: cr4bits->pvi-of-!cr4bits->pvi

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

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

(defthm !cr4bits->pvi-equiv-under-mask
  (b* ((?new-x (!cr4bits->pvi$inline pvi x)))
    (cr4bits-equiv-under-mask new-x x -3)))