		Search-engine friendly clone of the ACL2 documentation.

Cr4bits

!cr4bits->pke

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

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

Definitions and Theorems

Function: !cr4bits->pke$inline

(defun !cr4bits->pke$inline (pke x)
 (declare (xargs :guard (and (bitp pke) (cr4bits-p x))))
 (mbe
   :logic
   (b* ((pke (mbe :logic (bfix pke) :exec pke))
        (x (cr4bits-fix x)))
     (part-install pke x :width 1 :low 22))
   :exec (the (unsigned-byte 26)
              (logior (the (unsigned-byte 26)
                           (logand (the (unsigned-byte 26) x)
                                   (the (signed-byte 24) -4194305)))
                      (the (unsigned-byte 23)
                           (ash (the (unsigned-byte 1) pke)
                                22))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !cr4bits->pke-is-cr4bits

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

Theorem: cr4bits->pke-of-!cr4bits->pke

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

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

(defthm !cr4bits->pke-equiv-under-mask
  (b* ((?new-x (!cr4bits->pke$inline pke x)))
    (cr4bits-equiv-under-mask new-x x -4194305)))