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Ia32e-pml4ebits

Ia32e-pml4ebits->a

Access the |ACL2|::|A| field of a ia32e-pml4ebits bit structure.

Signature
(ia32e-pml4ebits->a x) → a
Arguments: x — Guard (ia32e-pml4ebits-p x).
Returns: a — Type (bitp a).

Definitions and Theorems

Function: ia32e-pml4ebits->a$inline

(defun ia32e-pml4ebits->a$inline (x)
 (declare (xargs :guard (ia32e-pml4ebits-p x)))
 (mbe
    :logic
    (let ((x (ia32e-pml4ebits-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-pml4ebits->a

(defthm bitp-of-ia32e-pml4ebits->a
  (b* ((a (ia32e-pml4ebits->a$inline x)))
    (bitp a))
  :rule-classes :rewrite)

Theorem: ia32e-pml4ebits->a$inline-of-ia32e-pml4ebits-fix-x

(defthm ia32e-pml4ebits->a$inline-of-ia32e-pml4ebits-fix-x
  (equal (ia32e-pml4ebits->a$inline (ia32e-pml4ebits-fix x))
         (ia32e-pml4ebits->a$inline x)))

Theorem: ia32e-pml4ebits->a$inline-ia32e-pml4ebits-equiv-congruence-on-x

(defthm
    ia32e-pml4ebits->a$inline-ia32e-pml4ebits-equiv-congruence-on-x
  (implies (ia32e-pml4ebits-equiv x x-equiv)
           (equal (ia32e-pml4ebits->a$inline x)
                  (ia32e-pml4ebits->a$inline x-equiv)))
  :rule-classes :congruence)

Theorem: ia32e-pml4ebits->a-of-ia32e-pml4ebits

(defthm ia32e-pml4ebits->a-of-ia32e-pml4ebits
  (equal (ia32e-pml4ebits->a
              (ia32e-pml4ebits p r/w u/s
                               pwt pcd a res1 ps res2 pdpt res3 xd))
         (bfix a)))

Theorem: ia32e-pml4ebits->a-of-write-with-mask

(defthm ia32e-pml4ebits->a-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x ia32e-pml4ebits-equiv-under-mask)
                (ia32e-pml4ebits-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 32)
                       0))
           (equal (ia32e-pml4ebits->a x)
                  (ia32e-pml4ebits->a y))))