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Cr3bits

!cr3bits->pcd

Update the |X86ISA|::|PCD| field of a cr3bits bit structure.

Signature
(!cr3bits->pcd pcd x) → new-x
Arguments: pcd — Guard (bitp pcd).; x — Guard (cr3bits-p x).
Returns: new-x — Type (cr3bits-p new-x).

Definitions and Theorems

Function: !cr3bits->pcd$inline

(defun !cr3bits->pcd$inline (pcd x)
 (declare (xargs :guard (and (bitp pcd) (cr3bits-p x))))
 (mbe
    :logic
    (b* ((pcd (mbe :logic (bfix pcd) :exec pcd))
         (x (cr3bits-fix x)))
      (part-install pcd x :width 1 :low 4))
    :exec (the (unsigned-byte 64)
               (logior (the (unsigned-byte 64)
                            (logand (the (unsigned-byte 64) x)
                                    (the (signed-byte 6) -17)))
                       (the (unsigned-byte 5)
                            (ash (the (unsigned-byte 1) pcd) 4))))))

Theorem: cr3bits-p-of-!cr3bits->pcd

(defthm cr3bits-p-of-!cr3bits->pcd
  (b* ((new-x (!cr3bits->pcd$inline pcd x)))
    (cr3bits-p new-x))
  :rule-classes :rewrite)

Theorem: !cr3bits->pcd$inline-of-bfix-pcd

(defthm !cr3bits->pcd$inline-of-bfix-pcd
  (equal (!cr3bits->pcd$inline (bfix pcd) x)
         (!cr3bits->pcd$inline pcd x)))

Theorem: !cr3bits->pcd$inline-bit-equiv-congruence-on-pcd

(defthm !cr3bits->pcd$inline-bit-equiv-congruence-on-pcd
  (implies (bit-equiv pcd pcd-equiv)
           (equal (!cr3bits->pcd$inline pcd x)
                  (!cr3bits->pcd$inline pcd-equiv x)))
  :rule-classes :congruence)

Theorem: !cr3bits->pcd$inline-of-cr3bits-fix-x

(defthm !cr3bits->pcd$inline-of-cr3bits-fix-x
  (equal (!cr3bits->pcd$inline pcd (cr3bits-fix x))
         (!cr3bits->pcd$inline pcd x)))

Theorem: !cr3bits->pcd$inline-cr3bits-equiv-congruence-on-x

(defthm !cr3bits->pcd$inline-cr3bits-equiv-congruence-on-x
  (implies (cr3bits-equiv x x-equiv)
           (equal (!cr3bits->pcd$inline pcd x)
                  (!cr3bits->pcd$inline pcd x-equiv)))
  :rule-classes :congruence)

Theorem: !cr3bits->pcd-is-cr3bits

(defthm !cr3bits->pcd-is-cr3bits
  (equal (!cr3bits->pcd pcd x)
         (change-cr3bits x :pcd pcd)))

Theorem: cr3bits->pcd-of-!cr3bits->pcd

(defthm cr3bits->pcd-of-!cr3bits->pcd
  (b* ((?new-x (!cr3bits->pcd$inline pcd x)))
    (equal (cr3bits->pcd new-x)
           (bfix pcd))))

Theorem: !cr3bits->pcd-equiv-under-mask

(defthm !cr3bits->pcd-equiv-under-mask
  (b* ((?new-x (!cr3bits->pcd$inline pcd x)))
    (cr3bits-equiv-under-mask new-x x -17)))