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Rflagsbits

!rflagsbits->rf

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

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

Definitions and Theorems

Function: !rflagsbits->rf$inline

(defun !rflagsbits->rf$inline (rf x)
 (declare (xargs :guard (and (bitp rf) (rflagsbits-p x))))
 (mbe
    :logic
    (b* ((rf (mbe :logic (bfix rf) :exec rf))
         (x (rflagsbits-fix x)))
      (part-install rf x :width 1 :low 16))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 18) -65537)))
                       (the (unsigned-byte 17)
                            (ash (the (unsigned-byte 1) rf) 16))))))

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

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

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

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

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

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

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

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

Theorem: !rflagsbits->rf$inline-rflagsbits-equiv-congruence-on-x

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

Theorem: !rflagsbits->rf-is-rflagsbits

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

Theorem: rflagsbits->rf-of-!rflagsbits->rf

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

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

(defthm !rflagsbits->rf-equiv-under-mask
  (b* ((?new-x (!rflagsbits->rf$inline rf x)))
    (rflagsbits-equiv-under-mask new-x x -65537)))