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Prefixes

!prefixes->num

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

Signature
(!prefixes->num num x) → new-x
Arguments: num — Guard (4bits-p num).; x — Guard (prefixes-p x).
Returns: new-x — Type (prefixes-p new-x).

Definitions and Theorems

Function: !prefixes->num$inline

(defun !prefixes->num$inline (num x)
  (declare (xargs :guard (and (4bits-p num) (prefixes-p x))))
  (mbe :logic
       (b* ((num (mbe :logic (4bits-fix num) :exec num))
            (x (prefixes-fix x)))
         (part-install num x :width 4 :low 0))
       :exec (the (unsigned-byte 52)
                  (logior (the (unsigned-byte 52)
                               (logand (the (unsigned-byte 52) x)
                                       (the (signed-byte 5) -16)))
                          (the (unsigned-byte 4) num)))))

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

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

Theorem: !prefixes->num$inline-of-4bits-fix-num

(defthm !prefixes->num$inline-of-4bits-fix-num
  (equal (!prefixes->num$inline (4bits-fix num)
                                x)
         (!prefixes->num$inline num x)))

Theorem: !prefixes->num$inline-4bits-equiv-congruence-on-num

(defthm !prefixes->num$inline-4bits-equiv-congruence-on-num
  (implies (4bits-equiv num num-equiv)
           (equal (!prefixes->num$inline num x)
                  (!prefixes->num$inline num-equiv x)))
  :rule-classes :congruence)

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

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

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

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

Theorem: !prefixes->num-is-prefixes

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

Theorem: prefixes->num-of-!prefixes->num

(defthm prefixes->num-of-!prefixes->num
  (b* ((?new-x (!prefixes->num$inline num x)))
    (equal (prefixes->num new-x)
           (4bits-fix num))))

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

(defthm !prefixes->num-equiv-under-mask
  (b* ((?new-x (!prefixes->num$inline num x)))
    (prefixes-equiv-under-mask new-x x -16)))