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Prefixes

!prefixes->seg

Update the |X86ISA|::|SEG| field of a prefixes bit structure.

Signature
(!prefixes->seg seg x) → new-x
Arguments: seg — Guard (8bits-p seg).; x — Guard (prefixes-p x).
Returns: new-x — Type (prefixes-p new-x).

Definitions and Theorems

Function: !prefixes->seg$inline

(defun !prefixes->seg$inline (seg x)
  (declare (xargs :guard (and (8bits-p seg) (prefixes-p x))))
  (mbe :logic
       (b* ((seg (mbe :logic (8bits-fix seg) :exec seg))
            (x (prefixes-fix x)))
         (part-install seg x :width 8 :low 20))
       :exec
       (the (unsigned-byte 52)
            (logior (the (unsigned-byte 52)
                         (logand (the (unsigned-byte 52) x)
                                 (the (signed-byte 29) -267386881)))
                    (the (unsigned-byte 28)
                         (ash (the (unsigned-byte 8) seg)
                              20))))))

Theorem: prefixes-p-of-!prefixes->seg

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

Theorem: !prefixes->seg$inline-of-8bits-fix-seg

(defthm !prefixes->seg$inline-of-8bits-fix-seg
  (equal (!prefixes->seg$inline (8bits-fix seg)
                                x)
         (!prefixes->seg$inline seg x)))

Theorem: !prefixes->seg$inline-8bits-equiv-congruence-on-seg

(defthm !prefixes->seg$inline-8bits-equiv-congruence-on-seg
  (implies (8bits-equiv seg seg-equiv)
           (equal (!prefixes->seg$inline seg x)
                  (!prefixes->seg$inline seg-equiv x)))
  :rule-classes :congruence)

Theorem: !prefixes->seg$inline-of-prefixes-fix-x

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

Theorem: !prefixes->seg$inline-prefixes-equiv-congruence-on-x

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

Theorem: !prefixes->seg-is-prefixes

(defthm !prefixes->seg-is-prefixes
  (equal (!prefixes->seg seg x)
         (change-prefixes x :seg seg)))

Theorem: prefixes->seg-of-!prefixes->seg

(defthm prefixes->seg-of-!prefixes->seg
  (b* ((?new-x (!prefixes->seg$inline seg x)))
    (equal (prefixes->seg new-x)
           (8bits-fix seg))))

Theorem: !prefixes->seg-equiv-under-mask

(defthm !prefixes->seg-equiv-under-mask
  (b* ((?new-x (!prefixes->seg$inline seg x)))
    (prefixes-equiv-under-mask new-x x -267386881)))