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Rflagsbits

!rflagsbits->zf

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

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

Definitions and Theorems

Function: !rflagsbits->zf$inline

(defun !rflagsbits->zf$inline (zf x)
 (declare (xargs :guard (and (bitp zf) (rflagsbits-p x))))
 (mbe
     :logic
     (b* ((zf (mbe :logic (bfix zf) :exec zf))
          (x (rflagsbits-fix x)))
       (part-install zf x :width 1 :low 6))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 8) -65)))
                        (the (unsigned-byte 7)
                             (ash (the (unsigned-byte 1) zf) 6))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !rflagsbits->zf-is-rflagsbits

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

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

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

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

(defthm !rflagsbits->zf-equiv-under-mask
  (b* ((?new-x (!rflagsbits->zf$inline zf x)))
    (rflagsbits-equiv-under-mask new-x x -65)))