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Cr3bits

Cr3bits->res1

Access the |X86ISA|::|RES1| field of a cr3bits bit structure.

Signature
(cr3bits->res1 x) → res1
Arguments: x — Guard (cr3bits-p x).
Returns: res1 — Type (3bits-p res1).

Definitions and Theorems

Function: cr3bits->res1$inline

(defun cr3bits->res1$inline (x)
  (declare (xargs :guard (cr3bits-p x)))
  (mbe :logic
       (let ((x (cr3bits-fix x)))
         (part-select x :low 0 :width 3))
       :exec (the (unsigned-byte 3)
                  (logand (the (unsigned-byte 3) 7)
                          (the (unsigned-byte 64) x)))))

Theorem: 3bits-p-of-cr3bits->res1

(defthm 3bits-p-of-cr3bits->res1
  (b* ((res1 (cr3bits->res1$inline x)))
    (3bits-p res1))
  :rule-classes :rewrite)

Theorem: cr3bits->res1$inline-of-cr3bits-fix-x

(defthm cr3bits->res1$inline-of-cr3bits-fix-x
  (equal (cr3bits->res1$inline (cr3bits-fix x))
         (cr3bits->res1$inline x)))

Theorem: cr3bits->res1$inline-cr3bits-equiv-congruence-on-x

(defthm cr3bits->res1$inline-cr3bits-equiv-congruence-on-x
  (implies (cr3bits-equiv x x-equiv)
           (equal (cr3bits->res1$inline x)
                  (cr3bits->res1$inline x-equiv)))
  :rule-classes :congruence)

Theorem: cr3bits->res1-of-cr3bits

(defthm cr3bits->res1-of-cr3bits
  (equal (cr3bits->res1 (cr3bits res1 pwt pcd res2 pdb res3))
         (3bits-fix res1)))

Theorem: cr3bits->res1-of-write-with-mask

(defthm cr3bits->res1-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) 7) 0))
  (equal (cr3bits->res1 x)
         (cr3bits->res1 y))))