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Cr4bits

!cr4bits->uintr

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

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

Definitions and Theorems

Function: !cr4bits->uintr$inline

(defun !cr4bits->uintr$inline (uintr x)
 (declare (xargs :guard (and (bitp uintr) (cr4bits-p x))))
 (mbe
  :logic
  (b* ((uintr (mbe :logic (bfix uintr) :exec uintr))
       (x (cr4bits-fix x)))
    (part-install uintr x :width 1 :low 25))
  :exec (the (unsigned-byte 26)
             (logior (the (unsigned-byte 26)
                          (logand (the (unsigned-byte 26) x)
                                  (the (signed-byte 27) -33554433)))
                     (the (unsigned-byte 26)
                          (ash (the (unsigned-byte 1) uintr)
                               25))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->uintr-is-cr4bits

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

Theorem: cr4bits->uintr-of-!cr4bits->uintr

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

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

(defthm !cr4bits->uintr-equiv-under-mask
  (b* ((?new-x (!cr4bits->uintr$inline uintr x)))
    (cr4bits-equiv-under-mask new-x x 33554431)))