		Search-engine friendly clone of the ACL2 documentation.

Ia32e-page-tablesbits

Ia32e-page-tablesbits->p

Access the |ACL2|::|P| field of a ia32e-page-tablesbits bit structure.

Signature
(ia32e-page-tablesbits->p x) → p
Arguments: x — Guard (ia32e-page-tablesbits-p x).
Returns: p — Type (bitp p).

Definitions and Theorems

Function: ia32e-page-tablesbits->p$inline

(defun ia32e-page-tablesbits->p$inline (x)
  (declare (xargs :guard (ia32e-page-tablesbits-p x)))
  (mbe :logic
       (let ((x (ia32e-page-tablesbits-fix x)))
         (part-select x :low 0 :width 1))
       :exec (the (unsigned-byte 1)
                  (logand (the (unsigned-byte 1) 1)
                          (the (unsigned-byte 64) x)))))

Theorem: bitp-of-ia32e-page-tablesbits->p

(defthm bitp-of-ia32e-page-tablesbits->p
  (b* ((p (ia32e-page-tablesbits->p$inline x)))
    (bitp p))
  :rule-classes :rewrite)

Theorem: ia32e-page-tablesbits->p$inline-of-ia32e-page-tablesbits-fix-x

(defthm
     ia32e-page-tablesbits->p$inline-of-ia32e-page-tablesbits-fix-x
 (equal
     (ia32e-page-tablesbits->p$inline (ia32e-page-tablesbits-fix x))
     (ia32e-page-tablesbits->p$inline x)))

Theorem: ia32e-page-tablesbits->p$inline-ia32e-page-tablesbits-equiv-congruence-on-x

(defthm
 ia32e-page-tablesbits->p$inline-ia32e-page-tablesbits-equiv-congruence-on-x
 (implies (ia32e-page-tablesbits-equiv x x-equiv)
          (equal (ia32e-page-tablesbits->p$inline x)
                 (ia32e-page-tablesbits->p$inline x-equiv)))
 :rule-classes :congruence)

Theorem: ia32e-page-tablesbits->p-of-ia32e-page-tablesbits

(defthm ia32e-page-tablesbits->p-of-ia32e-page-tablesbits
 (equal
  (ia32e-page-tablesbits->p
     (ia32e-page-tablesbits p r/w u/s pwt
                            pcd a d ps res1 reference-addr res2 xd))
  (bfix p)))

Theorem: ia32e-page-tablesbits->p-of-write-with-mask

(defthm ia32e-page-tablesbits->p-of-write-with-mask
  (implies
       (and (fty::bitstruct-read-over-write-hyps
                 x
                 ia32e-page-tablesbits-equiv-under-mask)
            (ia32e-page-tablesbits-equiv-under-mask x y fty::mask)
            (equal (logand (lognot fty::mask) 1) 0))
       (equal (ia32e-page-tablesbits->p x)
              (ia32e-page-tablesbits->p y))))