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Rflagsbits

Rflagsbits->cf

Access the |X86ISA|::|CF| field of a rflagsbits bit structure.

Signature
(rflagsbits->cf x) → cf
Arguments: x — Guard (rflagsbits-p x).
Returns: cf — Type (bitp cf).

Definitions and Theorems

Function: rflagsbits->cf$inline

(defun rflagsbits->cf$inline (x)
  (declare (xargs :guard (rflagsbits-p x)))
  (mbe :logic
       (let ((x (rflagsbits-fix x)))
         (part-select x :low 0 :width 1))
       :exec (the (unsigned-byte 1)
                  (logand (the (unsigned-byte 1) 1)
                          (the (unsigned-byte 32) x)))))

Theorem: bitp-of-rflagsbits->cf

(defthm bitp-of-rflagsbits->cf
  (b* ((cf (rflagsbits->cf$inline x)))
    (bitp cf))
  :rule-classes :rewrite)

Theorem: rflagsbits->cf$inline-of-rflagsbits-fix-x

(defthm rflagsbits->cf$inline-of-rflagsbits-fix-x
  (equal (rflagsbits->cf$inline (rflagsbits-fix x))
         (rflagsbits->cf$inline x)))

Theorem: rflagsbits->cf$inline-rflagsbits-equiv-congruence-on-x

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

Theorem: rflagsbits->cf-of-rflagsbits

(defthm rflagsbits->cf-of-rflagsbits
  (equal (rflagsbits->cf
              (rflagsbits cf
                          res1 pf res2 af res3 zf sf tf intf df of
                          iopl nt res4 rf vm ac vif vip id res5))
         (bfix cf)))

Theorem: rflagsbits->cf-of-write-with-mask

(defthm rflagsbits->cf-of-write-with-mask
  (implies (and (fty::bitstruct-read-over-write-hyps
                     x rflagsbits-equiv-under-mask)
                (rflagsbits-equiv-under-mask x y fty::mask)
                (equal (logand (lognot fty::mask) 1) 0))
           (equal (rflagsbits->cf x)
                  (rflagsbits->cf y))))