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Cr0bits

!cr0bits->et

Update the |X86ISA|::|ET| field of a cr0bits bit structure.

Signature
(!cr0bits->et et x) → new-x
Arguments: et — Guard (bitp et).; x — Guard (cr0bits-p x).
Returns: new-x — Type (cr0bits-p new-x).

Definitions and Theorems

Function: !cr0bits->et$inline

(defun !cr0bits->et$inline (et x)
 (declare (xargs :guard (and (bitp et) (cr0bits-p x))))
 (mbe
     :logic
     (b* ((et (mbe :logic (bfix et) :exec et))
          (x (cr0bits-fix x)))
       (part-install et x :width 1 :low 4))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 6) -17)))
                        (the (unsigned-byte 5)
                             (ash (the (unsigned-byte 1) et) 4))))))

Theorem: cr0bits-p-of-!cr0bits->et

(defthm cr0bits-p-of-!cr0bits->et
  (b* ((new-x (!cr0bits->et$inline et x)))
    (cr0bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr0bits->et$inline-of-bfix-et

(defthm !cr0bits->et$inline-of-bfix-et
  (equal (!cr0bits->et$inline (bfix et) x)
         (!cr0bits->et$inline et x)))

Theorem: !cr0bits->et$inline-bit-equiv-congruence-on-et

(defthm !cr0bits->et$inline-bit-equiv-congruence-on-et
  (implies (bit-equiv et et-equiv)
           (equal (!cr0bits->et$inline et x)
                  (!cr0bits->et$inline et-equiv x)))
  :rule-classes :congruence)

Theorem: !cr0bits->et$inline-of-cr0bits-fix-x

(defthm !cr0bits->et$inline-of-cr0bits-fix-x
  (equal (!cr0bits->et$inline et (cr0bits-fix x))
         (!cr0bits->et$inline et x)))

Theorem: !cr0bits->et$inline-cr0bits-equiv-congruence-on-x

(defthm !cr0bits->et$inline-cr0bits-equiv-congruence-on-x
  (implies (cr0bits-equiv x x-equiv)
           (equal (!cr0bits->et$inline et x)
                  (!cr0bits->et$inline et x-equiv)))
  :rule-classes :congruence)

Theorem: !cr0bits->et-is-cr0bits

(defthm !cr0bits->et-is-cr0bits
  (equal (!cr0bits->et et x)
         (change-cr0bits x :et et)))

Theorem: cr0bits->et-of-!cr0bits->et

(defthm cr0bits->et-of-!cr0bits->et
  (b* ((?new-x (!cr0bits->et$inline et x)))
    (equal (cr0bits->et new-x) (bfix et))))

Theorem: !cr0bits->et-equiv-under-mask

(defthm !cr0bits->et-equiv-under-mask
  (b* ((?new-x (!cr0bits->et$inline et x)))
    (cr0bits-equiv-under-mask new-x x -17)))