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Ia32e-page-tablesbits

Ia32e-page-tablesbits->a

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

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

Definitions and Theorems

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

(defun ia32e-page-tablesbits->a$inline (x)
 (declare (xargs :guard (ia32e-page-tablesbits-p x)))
 (mbe
    :logic
    (let ((x (ia32e-page-tablesbits-fix x)))
      (part-select x :low 5 :width 1))
    :exec (the (unsigned-byte 1)
               (logand (the (unsigned-byte 1) 1)
                       (the (unsigned-byte 59)
                            (ash (the (unsigned-byte 64) x) -5))))))

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

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

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

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

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

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

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

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

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

(defthm ia32e-page-tablesbits->a-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) 32)
                   0))
       (equal (ia32e-page-tablesbits->a x)
              (ia32e-page-tablesbits->a y))))