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Rflagsbits

!rflagsbits->of

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

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

Definitions and Theorems

Function: !rflagsbits->of$inline

(defun !rflagsbits->of$inline (of x)
 (declare (xargs :guard (and (bitp of) (rflagsbits-p x))))
 (mbe
    :logic
    (b* ((of (mbe :logic (bfix of) :exec of))
         (x (rflagsbits-fix x)))
      (part-install of x :width 1 :low 11))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 13) -2049)))
                       (the (unsigned-byte 12)
                            (ash (the (unsigned-byte 1) of) 11))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !rflagsbits->of-is-rflagsbits

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

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

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

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

(defthm !rflagsbits->of-equiv-under-mask
  (b* ((?new-x (!rflagsbits->of$inline of x)))
    (rflagsbits-equiv-under-mask new-x x -2049)))