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Rflagsbits

!rflagsbits->af

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

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

Definitions and Theorems

Function: !rflagsbits->af$inline

(defun !rflagsbits->af$inline (af x)
 (declare (xargs :guard (and (bitp af) (rflagsbits-p x))))
 (mbe
     :logic
     (b* ((af (mbe :logic (bfix af) :exec af))
          (x (rflagsbits-fix x)))
       (part-install af x :width 1 :low 4))
     :exec (the (unsigned-byte 32)
                (logior (the (unsigned-byte 32)
                             (logand (the (unsigned-byte 32) x)
                                     (the (signed-byte 6) -17)))
                        (the (unsigned-byte 5)
                             (ash (the (unsigned-byte 1) af) 4))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !rflagsbits->af-is-rflagsbits

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

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

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

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

(defthm !rflagsbits->af-equiv-under-mask
  (b* ((?new-x (!rflagsbits->af$inline af x)))
    (rflagsbits-equiv-under-mask new-x x -17)))