		Search-engine friendly clone of the ACL2 documentation.

Rflagsbits

!rflagsbits->cf

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

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

Definitions and Theorems

Function: !rflagsbits->cf$inline

(defun !rflagsbits->cf$inline (cf x)
  (declare (xargs :guard (and (bitp cf) (rflagsbits-p x))))
  (mbe :logic
       (b* ((cf (mbe :logic (bfix cf) :exec cf))
            (x (rflagsbits-fix x)))
         (part-install cf x :width 1 :low 0))
       :exec (the (unsigned-byte 32)
                  (logior (the (unsigned-byte 32)
                               (logand (the (unsigned-byte 32) x)
                                       (the (signed-byte 2) -2)))
                          (the (unsigned-byte 1) cf)))))

Theorem: rflagsbits-p-of-!rflagsbits->cf

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

Theorem: !rflagsbits->cf$inline-of-bfix-cf

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

Theorem: !rflagsbits->cf$inline-bit-equiv-congruence-on-cf

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

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

(defthm !rflagsbits->cf$inline-of-rflagsbits-fix-x
  (equal (!rflagsbits->cf$inline cf (rflagsbits-fix x))
         (!rflagsbits->cf$inline cf 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 cf x)
                  (!rflagsbits->cf$inline cf x-equiv)))
  :rule-classes :congruence)

Theorem: !rflagsbits->cf-is-rflagsbits

(defthm !rflagsbits->cf-is-rflagsbits
  (equal (!rflagsbits->cf cf x)
         (change-rflagsbits x :cf cf)))

Theorem: rflagsbits->cf-of-!rflagsbits->cf

(defthm rflagsbits->cf-of-!rflagsbits->cf
  (b* ((?new-x (!rflagsbits->cf$inline cf x)))
    (equal (rflagsbits->cf new-x)
           (bfix cf))))

Theorem: !rflagsbits->cf-equiv-under-mask

(defthm !rflagsbits->cf-equiv-under-mask
  (b* ((?new-x (!rflagsbits->cf$inline cf x)))
    (rflagsbits-equiv-under-mask new-x x -2)))