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Ia32e-pml4ebits

Ia32e-pml4ebits->res2

Access the |X86ISA|::|RES2| field of a ia32e-pml4ebits bit structure.

Signature
(ia32e-pml4ebits->res2 x) → res2
Arguments: x — Guard (ia32e-pml4ebits-p x).
Returns: res2 — Type (4bits-p res2).

Definitions and Theorems

Function: ia32e-pml4ebits->res2$inline

(defun ia32e-pml4ebits->res2$inline (x)
 (declare (xargs :guard (ia32e-pml4ebits-p x)))
 (mbe
    :logic
    (let ((x (ia32e-pml4ebits-fix x)))
      (part-select x :low 8 :width 4))
    :exec (the (unsigned-byte 4)
               (logand (the (unsigned-byte 4) 15)
                       (the (unsigned-byte 56)
                            (ash (the (unsigned-byte 64) x) -8))))))

Theorem: 4bits-p-of-ia32e-pml4ebits->res2

(defthm 4bits-p-of-ia32e-pml4ebits->res2
  (b* ((res2 (ia32e-pml4ebits->res2$inline x)))
    (4bits-p res2))
  :rule-classes :rewrite)

Theorem: ia32e-pml4ebits->res2$inline-of-ia32e-pml4ebits-fix-x

(defthm ia32e-pml4ebits->res2$inline-of-ia32e-pml4ebits-fix-x
  (equal (ia32e-pml4ebits->res2$inline (ia32e-pml4ebits-fix x))
         (ia32e-pml4ebits->res2$inline x)))

Theorem: ia32e-pml4ebits->res2$inline-ia32e-pml4ebits-equiv-congruence-on-x

(defthm
 ia32e-pml4ebits->res2$inline-ia32e-pml4ebits-equiv-congruence-on-x
 (implies (ia32e-pml4ebits-equiv x x-equiv)
          (equal (ia32e-pml4ebits->res2$inline x)
                 (ia32e-pml4ebits->res2$inline x-equiv)))
 :rule-classes :congruence)

Theorem: ia32e-pml4ebits->res2-of-ia32e-pml4ebits

(defthm ia32e-pml4ebits->res2-of-ia32e-pml4ebits
  (equal (ia32e-pml4ebits->res2
              (ia32e-pml4ebits p r/w u/s
                               pwt pcd a res1 ps res2 pdpt res3 xd))
         (4bits-fix res2)))

Theorem: ia32e-pml4ebits->res2-of-write-with-mask

(defthm ia32e-pml4ebits->res2-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) 3840)
                       0))
           (equal (ia32e-pml4ebits->res2 x)
                  (ia32e-pml4ebits->res2 y))))