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Cr3bits

Cr3bits->res3

Access the |X86ISA|::|RES3| field of a cr3bits bit structure.

Signature
(cr3bits->res3 x) → res3
Arguments: x — Guard (cr3bits-p x).
Returns: res3 — Type (12bits-p res3).

Definitions and Theorems

Function: cr3bits->res3$inline

(defun cr3bits->res3$inline (x)
  (declare (xargs :guard (cr3bits-p x)))
  (mbe :logic
       (let ((x (cr3bits-fix x)))
         (part-select x :low 52 :width 12))
       :exec (the (unsigned-byte 12)
                  (logand (the (unsigned-byte 12) 4095)
                          (the (unsigned-byte 12)
                               (ash (the (unsigned-byte 64) x)
                                    -52))))))

Theorem: 12bits-p-of-cr3bits->res3

(defthm 12bits-p-of-cr3bits->res3
  (b* ((res3 (cr3bits->res3$inline x)))
    (12bits-p res3))
  :rule-classes :rewrite)

Theorem: cr3bits->res3$inline-of-cr3bits-fix-x

(defthm cr3bits->res3$inline-of-cr3bits-fix-x
  (equal (cr3bits->res3$inline (cr3bits-fix x))
         (cr3bits->res3$inline x)))

Theorem: cr3bits->res3$inline-cr3bits-equiv-congruence-on-x

(defthm cr3bits->res3$inline-cr3bits-equiv-congruence-on-x
  (implies (cr3bits-equiv x x-equiv)
           (equal (cr3bits->res3$inline x)
                  (cr3bits->res3$inline x-equiv)))
  :rule-classes :congruence)

Theorem: cr3bits->res3-of-cr3bits

(defthm cr3bits->res3-of-cr3bits
  (equal (cr3bits->res3 (cr3bits res1 pwt pcd res2 pdb res3))
         (12bits-fix res3)))

Theorem: cr3bits->res3-of-write-with-mask

(defthm cr3bits->res3-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)
                   18442240474082181120)
           0))
  (equal (cr3bits->res3 x)
         (cr3bits->res3 y))))