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Cr4bits

!cr4bits->cet

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

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

Definitions and Theorems

Function: !cr4bits->cet$inline

(defun !cr4bits->cet$inline (cet x)
 (declare (xargs :guard (and (bitp cet) (cr4bits-p x))))
 (mbe
   :logic
   (b* ((cet (mbe :logic (bfix cet) :exec cet))
        (x (cr4bits-fix x)))
     (part-install cet x :width 1 :low 23))
   :exec (the (unsigned-byte 26)
              (logior (the (unsigned-byte 26)
                           (logand (the (unsigned-byte 26) x)
                                   (the (signed-byte 25) -8388609)))
                      (the (unsigned-byte 24)
                           (ash (the (unsigned-byte 1) cet)
                                23))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->cet-is-cr4bits

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

Theorem: cr4bits->cet-of-!cr4bits->cet

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

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

(defthm !cr4bits->cet-equiv-under-mask
  (b* ((?new-x (!cr4bits->cet$inline cet x)))
    (cr4bits-equiv-under-mask new-x x -8388609)))