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Cr0bits

!cr0bits->nw

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

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

Definitions and Theorems

Function: !cr0bits->nw$inline

(defun !cr0bits->nw$inline (nw x)
  (declare (xargs :guard (and (bitp nw) (cr0bits-p x))))
  (mbe :logic
       (b* ((nw (mbe :logic (bfix nw) :exec nw))
            (x (cr0bits-fix x)))
         (part-install nw x :width 1 :low 29))
       :exec
       (the (unsigned-byte 32)
            (logior (the (unsigned-byte 32)
                         (logand (the (unsigned-byte 32) x)
                                 (the (signed-byte 31) -536870913)))
                    (the (unsigned-byte 30)
                         (ash (the (unsigned-byte 1) nw) 29))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr0bits->nw-is-cr0bits

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

Theorem: cr0bits->nw-of-!cr0bits->nw

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

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

(defthm !cr0bits->nw-equiv-under-mask
  (b* ((?new-x (!cr0bits->nw$inline nw x)))
    (cr0bits-equiv-under-mask new-x x -536870913)))