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Prefixes

!prefixes->rep

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

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

Definitions and Theorems

Function: !prefixes->rep$inline

(defun !prefixes->rep$inline (rep x)
 (declare (xargs :guard (and (8bits-p rep) (prefixes-p x))))
 (mbe
   :logic
   (b* ((rep (mbe :logic (8bits-fix rep) :exec rep))
        (x (prefixes-fix x)))
     (part-install rep x :width 8 :low 12))
   :exec (the (unsigned-byte 52)
              (logior (the (unsigned-byte 52)
                           (logand (the (unsigned-byte 52) x)
                                   (the (signed-byte 21) -1044481)))
                      (the (unsigned-byte 20)
                           (ash (the (unsigned-byte 8) rep)
                                12))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !prefixes->rep-is-prefixes

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

Theorem: prefixes->rep-of-!prefixes->rep

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

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

(defthm !prefixes->rep-equiv-under-mask
  (b* ((?new-x (!prefixes->rep$inline rep x)))
    (prefixes-equiv-under-mask new-x x -1044481)))