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Cr4bits

!cr4bits->de

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

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

Definitions and Theorems

Function: !cr4bits->de$inline

(defun !cr4bits->de$inline (de x)
 (declare (xargs :guard (and (bitp de) (cr4bits-p x))))
 (mbe
     :logic
     (b* ((de (mbe :logic (bfix de) :exec de))
          (x (cr4bits-fix x)))
       (part-install de x :width 1 :low 3))
     :exec (the (unsigned-byte 26)
                (logior (the (unsigned-byte 26)
                             (logand (the (unsigned-byte 26) x)
                                     (the (signed-byte 5) -9)))
                        (the (unsigned-byte 4)
                             (ash (the (unsigned-byte 1) de) 3))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->de-is-cr4bits

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

Theorem: cr4bits->de-of-!cr4bits->de

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

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

(defthm !cr4bits->de-equiv-under-mask
  (b* ((?new-x (!cr4bits->de$inline de x)))
    (cr4bits-equiv-under-mask new-x x -9)))