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Cr3bits

Cr3bits->res2

Access the |X86ISA|::|RES2| field of a cr3bits bit structure.

Signature
(cr3bits->res2 x) → res2
Arguments: x — Guard (cr3bits-p x).
Returns: res2 — Type (7bits-p res2).

Definitions and Theorems

Function: cr3bits->res2$inline

(defun cr3bits->res2$inline (x)
 (declare (xargs :guard (cr3bits-p x)))
 (mbe
    :logic
    (let ((x (cr3bits-fix x)))
      (part-select x :low 5 :width 7))
    :exec (the (unsigned-byte 7)
               (logand (the (unsigned-byte 7) 127)
                       (the (unsigned-byte 59)
                            (ash (the (unsigned-byte 64) x) -5))))))

Theorem: 7bits-p-of-cr3bits->res2

(defthm 7bits-p-of-cr3bits->res2
  (b* ((res2 (cr3bits->res2$inline x)))
    (7bits-p res2))
  :rule-classes :rewrite)

Theorem: cr3bits->res2$inline-of-cr3bits-fix-x

(defthm cr3bits->res2$inline-of-cr3bits-fix-x
  (equal (cr3bits->res2$inline (cr3bits-fix x))
         (cr3bits->res2$inline x)))

Theorem: cr3bits->res2$inline-cr3bits-equiv-congruence-on-x

(defthm cr3bits->res2$inline-cr3bits-equiv-congruence-on-x
  (implies (cr3bits-equiv x x-equiv)
           (equal (cr3bits->res2$inline x)
                  (cr3bits->res2$inline x-equiv)))
  :rule-classes :congruence)

Theorem: cr3bits->res2-of-cr3bits

(defthm cr3bits->res2-of-cr3bits
  (equal (cr3bits->res2 (cr3bits res1 pwt pcd res2 pdb res3))
         (7bits-fix res2)))

Theorem: cr3bits->res2-of-write-with-mask

(defthm cr3bits->res2-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) 4064)
           0))
  (equal (cr3bits->res2 x)
         (cr3bits->res2 y))))