		Search-engine friendly clone of the ACL2 documentation.

Cr3bits

Cr3bits->pcd

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

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

Definitions and Theorems

Function: cr3bits->pcd$inline

(defun cr3bits->pcd$inline (x)
 (declare (xargs :guard (cr3bits-p x)))
 (mbe
    :logic
    (let ((x (cr3bits-fix x)))
      (part-select x :low 4 :width 1))
    :exec (the (unsigned-byte 1)
               (logand (the (unsigned-byte 1) 1)
                       (the (unsigned-byte 60)
                            (ash (the (unsigned-byte 64) x) -4))))))

Theorem: bitp-of-cr3bits->pcd

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

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

(defthm cr3bits->pcd$inline-of-cr3bits-fix-x
  (equal (cr3bits->pcd$inline (cr3bits-fix x))
         (cr3bits->pcd$inline 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 x)
                  (cr3bits->pcd$inline x-equiv)))
  :rule-classes :congruence)

Theorem: cr3bits->pcd-of-cr3bits

(defthm cr3bits->pcd-of-cr3bits
  (equal (cr3bits->pcd (cr3bits res1 pwt pcd res2 pdb res3))
         (bfix pcd)))

Theorem: cr3bits->pcd-of-write-with-mask

(defthm cr3bits->pcd-of-write-with-mask
 (implies
  (and
    (fty::bitstruct-read-over-write-hyps x cr3bits-equiv-under-mask)
    (cr3bits-equiv-under-mask x y fty::mask)
    (equal (logand (lognot fty::mask) 16)
           0))
  (equal (cr3bits->pcd x)
         (cr3bits->pcd y))))