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Prefixes

!prefixes->nxt

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

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

Definitions and Theorems

Function: !prefixes->nxt$inline

(defun !prefixes->nxt$inline (nxt x)
  (declare (xargs :guard (and (8bits-p nxt) (prefixes-p x))))
  (mbe :logic
       (b* ((nxt (mbe :logic (8bits-fix nxt) :exec nxt))
            (x (prefixes-fix x)))
         (part-install nxt x :width 8 :low 44))
       :exec (the (unsigned-byte 52)
                  (logior (the (unsigned-byte 52)
                               (logand (the (unsigned-byte 52) x)
                                       (the (signed-byte 53)
                                            -4486007441326081)))
                          (the (unsigned-byte 52)
                               (ash (the (unsigned-byte 8) nxt)
                                    44))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !prefixes->nxt-is-prefixes

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

Theorem: prefixes->nxt-of-!prefixes->nxt

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

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

(defthm !prefixes->nxt-equiv-under-mask
  (b* ((?new-x (!prefixes->nxt$inline nxt x)))
    (prefixes-equiv-under-mask new-x x 17592186044415)))