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Cr8bits

Cr8bits->cr8-trpl

Access the |X86ISA|::|CR8-TRPL| field of a cr8bits bit structure.

Signature
(cr8bits->cr8-trpl x) → cr8-trpl
Arguments: x — Guard (cr8bits-p x).
Returns: cr8-trpl — Type (4bits-p cr8-trpl).

Definitions and Theorems

Function: cr8bits->cr8-trpl$inline

(defun cr8bits->cr8-trpl$inline (x)
  (declare (xargs :guard (cr8bits-p x)))
  (mbe :logic
       (let ((x (cr8bits-fix x)))
         (part-select x :low 0 :width 4))
       :exec (the (unsigned-byte 4)
                  (logand (the (unsigned-byte 4) 15)
                          (the (unsigned-byte 4) x)))))

Theorem: 4bits-p-of-cr8bits->cr8-trpl

(defthm 4bits-p-of-cr8bits->cr8-trpl
  (b* ((cr8-trpl (cr8bits->cr8-trpl$inline x)))
    (4bits-p cr8-trpl))
  :rule-classes :rewrite)

Theorem: cr8bits->cr8-trpl$inline-of-cr8bits-fix-x

(defthm cr8bits->cr8-trpl$inline-of-cr8bits-fix-x
  (equal (cr8bits->cr8-trpl$inline (cr8bits-fix x))
         (cr8bits->cr8-trpl$inline x)))

Theorem: cr8bits->cr8-trpl$inline-cr8bits-equiv-congruence-on-x

(defthm cr8bits->cr8-trpl$inline-cr8bits-equiv-congruence-on-x
  (implies (cr8bits-equiv x x-equiv)
           (equal (cr8bits->cr8-trpl$inline x)
                  (cr8bits->cr8-trpl$inline x-equiv)))
  :rule-classes :congruence)

Theorem: cr8bits->cr8-trpl-of-cr8bits

(defthm cr8bits->cr8-trpl-of-cr8bits
  (equal (cr8bits->cr8-trpl (cr8bits cr8-trpl))
         (4bits-fix cr8-trpl)))

Theorem: cr8bits->cr8-trpl-of-write-with-mask

(defthm cr8bits->cr8-trpl-of-write-with-mask
 (implies
  (and
    (fty::bitstruct-read-over-write-hyps x cr8bits-equiv-under-mask)
    (cr8bits-equiv-under-mask x y fty::mask)
    (equal (logand (lognot fty::mask) 15)
           0))
  (equal (cr8bits->cr8-trpl x)
         (cr8bits->cr8-trpl y))))