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Rflagsbits

!rflagsbits->df

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

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

Definitions and Theorems

Function: !rflagsbits->df$inline

(defun !rflagsbits->df$inline (df x)
 (declare (xargs :guard (and (bitp df) (rflagsbits-p x))))
 (mbe
    :logic
    (b* ((df (mbe :logic (bfix df) :exec df))
         (x (rflagsbits-fix x)))
      (part-install df x :width 1 :low 10))
    :exec (the (unsigned-byte 32)
               (logior (the (unsigned-byte 32)
                            (logand (the (unsigned-byte 32) x)
                                    (the (signed-byte 12) -1025)))
                       (the (unsigned-byte 11)
                            (ash (the (unsigned-byte 1) df) 10))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !rflagsbits->df-is-rflagsbits

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

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

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

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

(defthm !rflagsbits->df-equiv-under-mask
  (b* ((?new-x (!rflagsbits->df$inline df x)))
    (rflagsbits-equiv-under-mask new-x x -1025)))