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Prefixes

!prefixes->lck

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

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

Definitions and Theorems

Function: !prefixes->lck$inline

(defun !prefixes->lck$inline (lck x)
 (declare (xargs :guard (and (8bits-p lck) (prefixes-p x))))
 (mbe
    :logic
    (b* ((lck (mbe :logic (8bits-fix lck) :exec lck))
         (x (prefixes-fix x)))
      (part-install lck x :width 8 :low 4))
    :exec (the (unsigned-byte 52)
               (logior (the (unsigned-byte 52)
                            (logand (the (unsigned-byte 52) x)
                                    (the (signed-byte 13) -4081)))
                       (the (unsigned-byte 12)
                            (ash (the (unsigned-byte 8) lck) 4))))))

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

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

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

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

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

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

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

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

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

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

Theorem: !prefixes->lck-is-prefixes

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

Theorem: prefixes->lck-of-!prefixes->lck

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

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

(defthm !prefixes->lck-equiv-under-mask
  (b* ((?new-x (!prefixes->lck$inline lck x)))
    (prefixes-equiv-under-mask new-x x -4081)))