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• Reasoning-about-memory-reads-and-writes

Las-to-pas

Signature

(las-to-pas n lin-addr r-w-x x86) → (mv flg p-addrs x86)

Arguments

n — Number of bytes to be read.
    Guard (natp n).

lin-addr — First linear address.
    Guard (integerp lin-addr).

r-w-x — Type of memory access: read, write, or execute.

Returns

p-addrs — Type (true-listp p-addrs).

x86 — Type (x86p x86), given (x86p x86).

Definitions and Theorems

Function: las-to-pas

(defun las-to-pas (n lin-addr r-w-x x86)
  (declare (xargs :stobjs (x86)))
  (declare (type (member :r :w :x) r-w-x))
  (declare (xargs :guard (and (natp n) (integerp lin-addr))))
  (declare (xargs :guard (not (app-view x86))))
  (let ((__function__ 'las-to-pas))
    (declare (ignorable __function__))
    (if (zp n)
        (mv nil nil x86)
      (b* (((unless (canonical-address-p lin-addr))
            (mv t nil x86))
           ((mv flg p-addr x86)
            (ia32e-la-to-pa lin-addr r-w-x x86))
           ((when flg) (mv flg nil x86))
           ((mv flgs p-addrs x86)
            (las-to-pas (1- n)
                        (1+ lin-addr)
                        r-w-x x86)))
        (mv flgs (if flgs nil (cons p-addr p-addrs))
            x86)))))

Theorem: true-listp-of-las-to-pas.p-addrs

(defthm true-listp-of-las-to-pas.p-addrs
  (b* (((mv ?flg ?p-addrs ?x86)
        (las-to-pas n lin-addr r-w-x x86)))
    (true-listp p-addrs))
  :rule-classes (:rewrite :type-prescription))

Theorem: x86p-of-las-to-pas.x86

(defthm x86p-of-las-to-pas.x86
  (implies (x86p x86)
           (b* (((mv ?flg ?p-addrs ?x86)
                 (las-to-pas n lin-addr r-w-x x86)))
             (x86p x86)))
  :rule-classes :rewrite)

Theorem: consp-mv-nth-1-las-to-pas

(defthm consp-mv-nth-1-las-to-pas
  (implies (and (not (mv-nth 0 (las-to-pas n lin-addr r-w-x x86)))
                (not (zp n)))
           (consp (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))
  :rule-classes (:rewrite :type-prescription))

Theorem: car-mv-nth-1-las-to-pas

(defthm car-mv-nth-1-las-to-pas
  (implies (and (not (mv-nth 0 (las-to-pas n lin-addr r-w-x x86)))
                (not (zp n)))
           (equal (car (mv-nth 1 (las-to-pas n lin-addr r-w-x x86)))
                  (mv-nth 1
                          (ia32e-la-to-pa lin-addr r-w-x x86)))))

Theorem: physical-address-listp-mv-nth-1-las-to-pas

(defthm physical-address-listp-mv-nth-1-las-to-pas
  (physical-address-listp
       (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: las-to-pas-n=0

(defthm las-to-pas-n=0
  (and (equal (mv-nth 0 (las-to-pas 0 lin-addr r-w-x x86))
              nil)
       (equal (mv-nth 1 (las-to-pas 0 lin-addr r-w-x x86))
              nil)
       (equal (mv-nth 2 (las-to-pas 0 lin-addr r-w-x x86))
              x86)))

Theorem: xr-ms-mv-nth-2-las-to-pas

(defthm xr-ms-mv-nth-2-las-to-pas
  (equal (xr :ms index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :ms index x86)))

Theorem: xr-env-mv-nth-2-las-to-pas

(defthm xr-env-mv-nth-2-las-to-pas
  (equal (xr :env index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :env index x86)))

Theorem: xr-undef-mv-nth-2-las-to-pas

(defthm xr-undef-mv-nth-2-las-to-pas
  (equal (xr :undef index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :undef index x86)))

Theorem: xr-app-view-mv-nth-2-las-to-pas

(defthm xr-app-view-mv-nth-2-las-to-pas
  (equal (xr :app-view index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :app-view index x86)))

Theorem: xr-marking-view-mv-nth-2-las-to-pas

(defthm xr-marking-view-mv-nth-2-las-to-pas
  (equal (xr :marking-view index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :marking-view index x86)))

Theorem: xr-enable-peripherals-mv-nth-2-las-to-pas

(defthm xr-enable-peripherals-mv-nth-2-las-to-pas
  (equal (xr :enable-peripherals index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :enable-peripherals index x86)))

Theorem: xr-handle-exceptions-mv-nth-2-las-to-pas

(defthm xr-handle-exceptions-mv-nth-2-las-to-pas
  (equal (xr :handle-exceptions index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :handle-exceptions index x86)))

Theorem: xr-os-info-mv-nth-2-las-to-pas

(defthm xr-os-info-mv-nth-2-las-to-pas
  (equal (xr :os-info index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :os-info index x86)))

Theorem: xr-rgf-mv-nth-2-las-to-pas

(defthm xr-rgf-mv-nth-2-las-to-pas
  (equal (xr :rgf index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :rgf index x86)))

Theorem: xr-rip-mv-nth-2-las-to-pas

(defthm xr-rip-mv-nth-2-las-to-pas
  (equal (xr :rip index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :rip index x86)))

Theorem: xr-rflags-mv-nth-2-las-to-pas

(defthm xr-rflags-mv-nth-2-las-to-pas
  (equal (xr :rflags index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :rflags index x86)))

Theorem: xr-seg-visible-mv-nth-2-las-to-pas

(defthm xr-seg-visible-mv-nth-2-las-to-pas
  (equal (xr :seg-visible index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :seg-visible index x86)))

Theorem: xr-seg-hidden-base-mv-nth-2-las-to-pas

(defthm xr-seg-hidden-base-mv-nth-2-las-to-pas
  (equal (xr :seg-hidden-base index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :seg-hidden-base index x86)))

Theorem: xr-seg-hidden-limit-mv-nth-2-las-to-pas

(defthm xr-seg-hidden-limit-mv-nth-2-las-to-pas
  (equal (xr :seg-hidden-limit index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :seg-hidden-limit index x86)))

Theorem: xr-seg-hidden-attr-mv-nth-2-las-to-pas

(defthm xr-seg-hidden-attr-mv-nth-2-las-to-pas
  (equal (xr :seg-hidden-attr index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :seg-hidden-attr index x86)))

Theorem: xr-str-mv-nth-2-las-to-pas

(defthm xr-str-mv-nth-2-las-to-pas
  (equal (xr :str index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :str index x86)))

Theorem: xr-ssr-visible-mv-nth-2-las-to-pas

(defthm xr-ssr-visible-mv-nth-2-las-to-pas
  (equal (xr :ssr-visible index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :ssr-visible index x86)))

Theorem: xr-ssr-hidden-base-mv-nth-2-las-to-pas

(defthm xr-ssr-hidden-base-mv-nth-2-las-to-pas
  (equal (xr :ssr-hidden-base index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :ssr-hidden-base index x86)))

Theorem: xr-ssr-hidden-limit-mv-nth-2-las-to-pas

(defthm xr-ssr-hidden-limit-mv-nth-2-las-to-pas
  (equal (xr :ssr-hidden-limit index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :ssr-hidden-limit index x86)))

Theorem: xr-ssr-hidden-attr-mv-nth-2-las-to-pas

(defthm xr-ssr-hidden-attr-mv-nth-2-las-to-pas
  (equal (xr :ssr-hidden-attr index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :ssr-hidden-attr index x86)))

Theorem: xr-ctr-mv-nth-2-las-to-pas

(defthm xr-ctr-mv-nth-2-las-to-pas
  (equal (xr :ctr index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :ctr index x86)))

Theorem: xr-dbg-mv-nth-2-las-to-pas

(defthm xr-dbg-mv-nth-2-las-to-pas
  (equal (xr :dbg index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :dbg index x86)))

Theorem: xr-fp-data-mv-nth-2-las-to-pas

(defthm xr-fp-data-mv-nth-2-las-to-pas
  (equal (xr :fp-data index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :fp-data index x86)))

Theorem: xr-fp-ctrl-mv-nth-2-las-to-pas

(defthm xr-fp-ctrl-mv-nth-2-las-to-pas
  (equal (xr :fp-ctrl index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :fp-ctrl index x86)))

Theorem: xr-fp-status-mv-nth-2-las-to-pas

(defthm xr-fp-status-mv-nth-2-las-to-pas
  (equal (xr :fp-status index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :fp-status index x86)))

Theorem: xr-fp-tag-mv-nth-2-las-to-pas

(defthm xr-fp-tag-mv-nth-2-las-to-pas
  (equal (xr :fp-tag index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :fp-tag index x86)))

Theorem: xr-fp-last-inst-mv-nth-2-las-to-pas

(defthm xr-fp-last-inst-mv-nth-2-las-to-pas
  (equal (xr :fp-last-inst index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :fp-last-inst index x86)))

Theorem: xr-fp-last-data-mv-nth-2-las-to-pas

(defthm xr-fp-last-data-mv-nth-2-las-to-pas
  (equal (xr :fp-last-data index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :fp-last-data index x86)))

Theorem: xr-fp-opcode-mv-nth-2-las-to-pas

(defthm xr-fp-opcode-mv-nth-2-las-to-pas
  (equal (xr :fp-opcode index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :fp-opcode index x86)))

Theorem: xr-mxcsr-mv-nth-2-las-to-pas

(defthm xr-mxcsr-mv-nth-2-las-to-pas
  (equal (xr :mxcsr index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :mxcsr index x86)))

Theorem: xr-opmsk-mv-nth-2-las-to-pas

(defthm xr-opmsk-mv-nth-2-las-to-pas
  (equal (xr :opmsk index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :opmsk index x86)))

Theorem: xr-zmm-mv-nth-2-las-to-pas

(defthm xr-zmm-mv-nth-2-las-to-pas
  (equal (xr :zmm index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :zmm index x86)))

Theorem: xr-msr-mv-nth-2-las-to-pas

(defthm xr-msr-mv-nth-2-las-to-pas
  (equal (xr :msr index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :msr index x86)))

Theorem: xr-inhibit-interrupts-one-instruction-mv-nth-2-las-to-pas

(defthm xr-inhibit-interrupts-one-instruction-mv-nth-2-las-to-pas
  (equal (xr :inhibit-interrupts-one-instruction
             index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :inhibit-interrupts-one-instruction
             index x86)))

Theorem: xr-time-stamp-counter-mv-nth-2-las-to-pas

(defthm xr-time-stamp-counter-mv-nth-2-las-to-pas
  (equal (xr :time-stamp-counter index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :time-stamp-counter index x86)))

Theorem: xr-last-clock-event-mv-nth-2-las-to-pas

(defthm xr-last-clock-event-mv-nth-2-las-to-pas
  (equal (xr :last-clock-event index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :last-clock-event index x86)))

Theorem: xr-implicit-supervisor-access-mv-nth-2-las-to-pas

(defthm xr-implicit-supervisor-access-mv-nth-2-las-to-pas
  (equal (xr :implicit-supervisor-access index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :implicit-supervisor-access index x86)))

Theorem: xr-tty-in-mv-nth-2-las-to-pas

(defthm xr-tty-in-mv-nth-2-las-to-pas
  (equal (xr :tty-in index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :tty-in index x86)))

Theorem: xr-tty-out-mv-nth-2-las-to-pas

(defthm xr-tty-out-mv-nth-2-las-to-pas
  (equal (xr :tty-out index
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (xr :tty-out index x86)))

Theorem: xr-rflags-las-to-pas

(defthm xr-rflags-las-to-pas
 (implies
   (not (mv-nth 0
                (las-to-pas n lin-addr r-w-x (double-rewrite x86))))
   (equal (xr :rflags nil
              (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
          (xr :rflags nil (double-rewrite x86)))))

Theorem: xr-fault-las-to-pas

(defthm xr-fault-las-to-pas
 (implies
   (not (mv-nth 0
                (las-to-pas n lin-addr r-w-x (double-rewrite x86))))
   (equal (xr :fault nil
              (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
          (xr :fault nil (double-rewrite x86)))))

Theorem: mv-nth-0-las-to-pas-xw-ms

(defthm mv-nth-0-las-to-pas-xw-ms
  (equal (mv-nth 0
                 (las-to-pas n
                             lin-addr r-w-x (xw :ms index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-env

(defthm mv-nth-0-las-to-pas-xw-env
 (equal (mv-nth 0
                (las-to-pas n
                            lin-addr r-w-x (xw :env index val x86)))
        (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-undef

(defthm mv-nth-0-las-to-pas-xw-undef
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :undef index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-enable-peripherals

(defthm mv-nth-0-las-to-pas-xw-enable-peripherals
 (equal (mv-nth 0
                (las-to-pas n lin-addr r-w-x
                            (xw :enable-peripherals index val x86)))
        (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-handle-exceptions

(defthm mv-nth-0-las-to-pas-xw-handle-exceptions
  (equal (mv-nth 0
                 (las-to-pas n lin-addr r-w-x
                             (xw :handle-exceptions index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-os-info

(defthm mv-nth-0-las-to-pas-xw-os-info
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :os-info index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-rgf

(defthm mv-nth-0-las-to-pas-xw-rgf
 (equal (mv-nth 0
                (las-to-pas n
                            lin-addr r-w-x (xw :rgf index val x86)))
        (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-rip

(defthm mv-nth-0-las-to-pas-xw-rip
 (equal (mv-nth 0
                (las-to-pas n
                            lin-addr r-w-x (xw :rip index val x86)))
        (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-seg-hidden-base

(defthm mv-nth-0-las-to-pas-xw-seg-hidden-base
  (equal (mv-nth 0
                 (las-to-pas n lin-addr r-w-x
                             (xw :seg-hidden-base index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-seg-hidden-limit

(defthm mv-nth-0-las-to-pas-xw-seg-hidden-limit
  (equal (mv-nth 0
                 (las-to-pas n lin-addr r-w-x
                             (xw :seg-hidden-limit index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-seg-hidden-attr

(defthm mv-nth-0-las-to-pas-xw-seg-hidden-attr
  (equal (mv-nth 0
                 (las-to-pas n lin-addr r-w-x
                             (xw :seg-hidden-attr index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-str

(defthm mv-nth-0-las-to-pas-xw-str
 (equal (mv-nth 0
                (las-to-pas n
                            lin-addr r-w-x (xw :str index val x86)))
        (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-ssr-visible

(defthm mv-nth-0-las-to-pas-xw-ssr-visible
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :ssr-visible index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-ssr-hidden-base

(defthm mv-nth-0-las-to-pas-xw-ssr-hidden-base
  (equal (mv-nth 0
                 (las-to-pas n lin-addr r-w-x
                             (xw :ssr-hidden-base index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-ssr-hidden-limit

(defthm mv-nth-0-las-to-pas-xw-ssr-hidden-limit
  (equal (mv-nth 0
                 (las-to-pas n lin-addr r-w-x
                             (xw :ssr-hidden-limit index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-ssr-hidden-attr

(defthm mv-nth-0-las-to-pas-xw-ssr-hidden-attr
  (equal (mv-nth 0
                 (las-to-pas n lin-addr r-w-x
                             (xw :ssr-hidden-attr index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-dbg

(defthm mv-nth-0-las-to-pas-xw-dbg
 (equal (mv-nth 0
                (las-to-pas n
                            lin-addr r-w-x (xw :dbg index val x86)))
        (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-fp-data

(defthm mv-nth-0-las-to-pas-xw-fp-data
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-data index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-fp-ctrl

(defthm mv-nth-0-las-to-pas-xw-fp-ctrl
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-ctrl index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-fp-status

(defthm mv-nth-0-las-to-pas-xw-fp-status
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-status index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-fp-tag

(defthm mv-nth-0-las-to-pas-xw-fp-tag
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-tag index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-fp-last-inst

(defthm mv-nth-0-las-to-pas-xw-fp-last-inst
 (equal (mv-nth 0
                (las-to-pas n lin-addr
                            r-w-x (xw :fp-last-inst index val x86)))
        (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-fp-last-data

(defthm mv-nth-0-las-to-pas-xw-fp-last-data
 (equal (mv-nth 0
                (las-to-pas n lin-addr
                            r-w-x (xw :fp-last-data index val x86)))
        (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-fp-opcode

(defthm mv-nth-0-las-to-pas-xw-fp-opcode
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-opcode index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-mxcsr

(defthm mv-nth-0-las-to-pas-xw-mxcsr
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :mxcsr index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-opmsk

(defthm mv-nth-0-las-to-pas-xw-opmsk
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :opmsk index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-zmm

(defthm mv-nth-0-las-to-pas-xw-zmm
 (equal (mv-nth 0
                (las-to-pas n
                            lin-addr r-w-x (xw :zmm index val x86)))
        (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-inhibit-interrupts-one-instruction

(defthm mv-nth-0-las-to-pas-xw-inhibit-interrupts-one-instruction
  (equal (mv-nth 0
                 (las-to-pas n lin-addr r-w-x
                             (xw :inhibit-interrupts-one-instruction
                                 index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-time-stamp-counter

(defthm mv-nth-0-las-to-pas-xw-time-stamp-counter
 (equal (mv-nth 0
                (las-to-pas n lin-addr r-w-x
                            (xw :time-stamp-counter index val x86)))
        (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-last-clock-event

(defthm mv-nth-0-las-to-pas-xw-last-clock-event
  (equal (mv-nth 0
                 (las-to-pas n lin-addr r-w-x
                             (xw :last-clock-event index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-tty-in

(defthm mv-nth-0-las-to-pas-xw-tty-in
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :tty-in index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-0-las-to-pas-xw-tty-out

(defthm mv-nth-0-las-to-pas-xw-tty-out
  (equal (mv-nth 0
                 (las-to-pas n lin-addr
                             r-w-x (xw :tty-out index val x86)))
         (mv-nth 0 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-ms

(defthm mv-nth-1-las-to-pas-xw-ms
  (equal (mv-nth 1
                 (las-to-pas n
                             lin-addr r-w-x (xw :ms index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-env

(defthm mv-nth-1-las-to-pas-xw-env
 (equal (mv-nth 1
                (las-to-pas n
                            lin-addr r-w-x (xw :env index val x86)))
        (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-undef

(defthm mv-nth-1-las-to-pas-xw-undef
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :undef index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-enable-peripherals

(defthm mv-nth-1-las-to-pas-xw-enable-peripherals
 (equal (mv-nth 1
                (las-to-pas n lin-addr r-w-x
                            (xw :enable-peripherals index val x86)))
        (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-handle-exceptions

(defthm mv-nth-1-las-to-pas-xw-handle-exceptions
  (equal (mv-nth 1
                 (las-to-pas n lin-addr r-w-x
                             (xw :handle-exceptions index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-os-info

(defthm mv-nth-1-las-to-pas-xw-os-info
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :os-info index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-rgf

(defthm mv-nth-1-las-to-pas-xw-rgf
 (equal (mv-nth 1
                (las-to-pas n
                            lin-addr r-w-x (xw :rgf index val x86)))
        (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-rip

(defthm mv-nth-1-las-to-pas-xw-rip
 (equal (mv-nth 1
                (las-to-pas n
                            lin-addr r-w-x (xw :rip index val x86)))
        (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-seg-hidden-base

(defthm mv-nth-1-las-to-pas-xw-seg-hidden-base
  (equal (mv-nth 1
                 (las-to-pas n lin-addr r-w-x
                             (xw :seg-hidden-base index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-seg-hidden-limit

(defthm mv-nth-1-las-to-pas-xw-seg-hidden-limit
  (equal (mv-nth 1
                 (las-to-pas n lin-addr r-w-x
                             (xw :seg-hidden-limit index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-seg-hidden-attr

(defthm mv-nth-1-las-to-pas-xw-seg-hidden-attr
  (equal (mv-nth 1
                 (las-to-pas n lin-addr r-w-x
                             (xw :seg-hidden-attr index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-str

(defthm mv-nth-1-las-to-pas-xw-str
 (equal (mv-nth 1
                (las-to-pas n
                            lin-addr r-w-x (xw :str index val x86)))
        (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-ssr-visible

(defthm mv-nth-1-las-to-pas-xw-ssr-visible
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :ssr-visible index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-ssr-hidden-base

(defthm mv-nth-1-las-to-pas-xw-ssr-hidden-base
  (equal (mv-nth 1
                 (las-to-pas n lin-addr r-w-x
                             (xw :ssr-hidden-base index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-ssr-hidden-limit

(defthm mv-nth-1-las-to-pas-xw-ssr-hidden-limit
  (equal (mv-nth 1
                 (las-to-pas n lin-addr r-w-x
                             (xw :ssr-hidden-limit index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-ssr-hidden-attr

(defthm mv-nth-1-las-to-pas-xw-ssr-hidden-attr
  (equal (mv-nth 1
                 (las-to-pas n lin-addr r-w-x
                             (xw :ssr-hidden-attr index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-dbg

(defthm mv-nth-1-las-to-pas-xw-dbg
 (equal (mv-nth 1
                (las-to-pas n
                            lin-addr r-w-x (xw :dbg index val x86)))
        (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-fp-data

(defthm mv-nth-1-las-to-pas-xw-fp-data
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-data index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-fp-ctrl

(defthm mv-nth-1-las-to-pas-xw-fp-ctrl
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-ctrl index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-fp-status

(defthm mv-nth-1-las-to-pas-xw-fp-status
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-status index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-fp-tag

(defthm mv-nth-1-las-to-pas-xw-fp-tag
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-tag index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-fp-last-inst

(defthm mv-nth-1-las-to-pas-xw-fp-last-inst
 (equal (mv-nth 1
                (las-to-pas n lin-addr
                            r-w-x (xw :fp-last-inst index val x86)))
        (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-fp-last-data

(defthm mv-nth-1-las-to-pas-xw-fp-last-data
 (equal (mv-nth 1
                (las-to-pas n lin-addr
                            r-w-x (xw :fp-last-data index val x86)))
        (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-fp-opcode

(defthm mv-nth-1-las-to-pas-xw-fp-opcode
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-opcode index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-mxcsr

(defthm mv-nth-1-las-to-pas-xw-mxcsr
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :mxcsr index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-opmsk

(defthm mv-nth-1-las-to-pas-xw-opmsk
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :opmsk index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-zmm

(defthm mv-nth-1-las-to-pas-xw-zmm
 (equal (mv-nth 1
                (las-to-pas n
                            lin-addr r-w-x (xw :zmm index val x86)))
        (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-inhibit-interrupts-one-instruction

(defthm mv-nth-1-las-to-pas-xw-inhibit-interrupts-one-instruction
  (equal (mv-nth 1
                 (las-to-pas n lin-addr r-w-x
                             (xw :inhibit-interrupts-one-instruction
                                 index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-time-stamp-counter

(defthm mv-nth-1-las-to-pas-xw-time-stamp-counter
 (equal (mv-nth 1
                (las-to-pas n lin-addr r-w-x
                            (xw :time-stamp-counter index val x86)))
        (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-last-clock-event

(defthm mv-nth-1-las-to-pas-xw-last-clock-event
  (equal (mv-nth 1
                 (las-to-pas n lin-addr r-w-x
                             (xw :last-clock-event index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-tty-in

(defthm mv-nth-1-las-to-pas-xw-tty-in
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :tty-in index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: mv-nth-1-las-to-pas-xw-tty-out

(defthm mv-nth-1-las-to-pas-xw-tty-out
  (equal (mv-nth 1
                 (las-to-pas n lin-addr
                             r-w-x (xw :tty-out index val x86)))
         (mv-nth 1 (las-to-pas n lin-addr r-w-x x86))))

Theorem: 64-bit-modep-of-las-to-pas

(defthm 64-bit-modep-of-las-to-pas
  (equal (64-bit-modep (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
         (64-bit-modep x86)))

Theorem: x86-operation-mode-of-las-to-pas

(defthm x86-operation-mode-of-las-to-pas
 (equal
   (x86-operation-mode (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))
   (x86-operation-mode x86)))

Theorem: mv-nth-2-las-to-pas-xw-ms

(defthm mv-nth-2-las-to-pas-xw-ms
  (equal (mv-nth 2
                 (las-to-pas n
                             lin-addr r-w-x (xw :ms index val x86)))
         (xw :ms index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-env

(defthm mv-nth-2-las-to-pas-xw-env
 (equal (mv-nth 2
                (las-to-pas n
                            lin-addr r-w-x (xw :env index val x86)))
        (xw :env index val
            (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-undef

(defthm mv-nth-2-las-to-pas-xw-undef
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :undef index val x86)))
         (xw :undef index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-enable-peripherals

(defthm mv-nth-2-las-to-pas-xw-enable-peripherals
 (equal (mv-nth 2
                (las-to-pas n lin-addr r-w-x
                            (xw :enable-peripherals index val x86)))
        (xw :enable-peripherals index val
            (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-handle-exceptions

(defthm mv-nth-2-las-to-pas-xw-handle-exceptions
  (equal (mv-nth 2
                 (las-to-pas n lin-addr r-w-x
                             (xw :handle-exceptions index val x86)))
         (xw :handle-exceptions index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-os-info

(defthm mv-nth-2-las-to-pas-xw-os-info
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :os-info index val x86)))
         (xw :os-info index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-rgf

(defthm mv-nth-2-las-to-pas-xw-rgf
 (equal (mv-nth 2
                (las-to-pas n
                            lin-addr r-w-x (xw :rgf index val x86)))
        (xw :rgf index val
            (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-rip

(defthm mv-nth-2-las-to-pas-xw-rip
 (equal (mv-nth 2
                (las-to-pas n
                            lin-addr r-w-x (xw :rip index val x86)))
        (xw :rip index val
            (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-seg-hidden-base

(defthm mv-nth-2-las-to-pas-xw-seg-hidden-base
  (equal (mv-nth 2
                 (las-to-pas n lin-addr r-w-x
                             (xw :seg-hidden-base index val x86)))
         (xw :seg-hidden-base index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-seg-hidden-limit

(defthm mv-nth-2-las-to-pas-xw-seg-hidden-limit
  (equal (mv-nth 2
                 (las-to-pas n lin-addr r-w-x
                             (xw :seg-hidden-limit index val x86)))
         (xw :seg-hidden-limit index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-seg-hidden-attr

(defthm mv-nth-2-las-to-pas-xw-seg-hidden-attr
  (equal (mv-nth 2
                 (las-to-pas n lin-addr r-w-x
                             (xw :seg-hidden-attr index val x86)))
         (xw :seg-hidden-attr index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-str

(defthm mv-nth-2-las-to-pas-xw-str
 (equal (mv-nth 2
                (las-to-pas n
                            lin-addr r-w-x (xw :str index val x86)))
        (xw :str index val
            (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-ssr-visible

(defthm mv-nth-2-las-to-pas-xw-ssr-visible
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :ssr-visible index val x86)))
         (xw :ssr-visible index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-ssr-hidden-base

(defthm mv-nth-2-las-to-pas-xw-ssr-hidden-base
  (equal (mv-nth 2
                 (las-to-pas n lin-addr r-w-x
                             (xw :ssr-hidden-base index val x86)))
         (xw :ssr-hidden-base index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-ssr-hidden-limit

(defthm mv-nth-2-las-to-pas-xw-ssr-hidden-limit
  (equal (mv-nth 2
                 (las-to-pas n lin-addr r-w-x
                             (xw :ssr-hidden-limit index val x86)))
         (xw :ssr-hidden-limit index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-ssr-hidden-attr

(defthm mv-nth-2-las-to-pas-xw-ssr-hidden-attr
  (equal (mv-nth 2
                 (las-to-pas n lin-addr r-w-x
                             (xw :ssr-hidden-attr index val x86)))
         (xw :ssr-hidden-attr index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-dbg

(defthm mv-nth-2-las-to-pas-xw-dbg
 (equal (mv-nth 2
                (las-to-pas n
                            lin-addr r-w-x (xw :dbg index val x86)))
        (xw :dbg index val
            (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-fp-data

(defthm mv-nth-2-las-to-pas-xw-fp-data
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-data index val x86)))
         (xw :fp-data index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-fp-ctrl

(defthm mv-nth-2-las-to-pas-xw-fp-ctrl
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-ctrl index val x86)))
         (xw :fp-ctrl index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-fp-status

(defthm mv-nth-2-las-to-pas-xw-fp-status
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-status index val x86)))
         (xw :fp-status index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-fp-tag

(defthm mv-nth-2-las-to-pas-xw-fp-tag
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-tag index val x86)))
         (xw :fp-tag index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-fp-last-inst

(defthm mv-nth-2-las-to-pas-xw-fp-last-inst
 (equal (mv-nth 2
                (las-to-pas n lin-addr
                            r-w-x (xw :fp-last-inst index val x86)))
        (xw :fp-last-inst index val
            (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-fp-last-data

(defthm mv-nth-2-las-to-pas-xw-fp-last-data
 (equal (mv-nth 2
                (las-to-pas n lin-addr
                            r-w-x (xw :fp-last-data index val x86)))
        (xw :fp-last-data index val
            (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-fp-opcode

(defthm mv-nth-2-las-to-pas-xw-fp-opcode
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :fp-opcode index val x86)))
         (xw :fp-opcode index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-mxcsr

(defthm mv-nth-2-las-to-pas-xw-mxcsr
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :mxcsr index val x86)))
         (xw :mxcsr index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-opmsk

(defthm mv-nth-2-las-to-pas-xw-opmsk
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :opmsk index val x86)))
         (xw :opmsk index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-zmm

(defthm mv-nth-2-las-to-pas-xw-zmm
 (equal (mv-nth 2
                (las-to-pas n
                            lin-addr r-w-x (xw :zmm index val x86)))
        (xw :zmm index val
            (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-inhibit-interrupts-one-instruction

(defthm mv-nth-2-las-to-pas-xw-inhibit-interrupts-one-instruction
  (equal (mv-nth 2
                 (las-to-pas n lin-addr r-w-x
                             (xw :inhibit-interrupts-one-instruction
                                 index val x86)))
         (xw :inhibit-interrupts-one-instruction
             index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-time-stamp-counter

(defthm mv-nth-2-las-to-pas-xw-time-stamp-counter
 (equal (mv-nth 2
                (las-to-pas n lin-addr r-w-x
                            (xw :time-stamp-counter index val x86)))
        (xw :time-stamp-counter index val
            (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-last-clock-event

(defthm mv-nth-2-las-to-pas-xw-last-clock-event
  (equal (mv-nth 2
                 (las-to-pas n lin-addr r-w-x
                             (xw :last-clock-event index val x86)))
         (xw :last-clock-event index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-tty-in

(defthm mv-nth-2-las-to-pas-xw-tty-in
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :tty-in index val x86)))
         (xw :tty-in index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: mv-nth-2-las-to-pas-xw-tty-out

(defthm mv-nth-2-las-to-pas-xw-tty-out
  (equal (mv-nth 2
                 (las-to-pas n lin-addr
                             r-w-x (xw :tty-out index val x86)))
         (xw :tty-out index val
             (mv-nth 2 (las-to-pas n lin-addr r-w-x x86)))))

Theorem: las-to-pas-xw-rflags-not-ac

(defthm las-to-pas-xw-rflags-not-ac
 (implies
  (equal (rflagsbits->ac value)
         (rflagsbits->ac (rflags (double-rewrite x86))))
  (and
   (equal
        (mv-nth 0
                (las-to-pas n lin-addr
                            r-w-x (xw :rflags nil value x86)))
        (mv-nth 0
                (las-to-pas n lin-addr r-w-x (double-rewrite x86))))
   (equal (mv-nth 1
                  (las-to-pas n lin-addr
                              r-w-x (xw :rflags nil value x86)))
          (mv-nth 1
                  (las-to-pas n lin-addr
                              r-w-x (double-rewrite x86)))))))

Theorem: las-to-pas-xw-rflags-state-not-ac

(defthm las-to-pas-xw-rflags-state-not-ac
  (implies
       (equal (rflagsbits->ac value)
              (rflagsbits->ac (rflags x86)))
       (equal (mv-nth 2
                      (las-to-pas n lin-addr
                                  r-w-x (xw :rflags nil value x86)))
              (xw :rflags nil value
                  (mv-nth 2 (las-to-pas n lin-addr r-w-x x86))))))

Theorem: len-of-mv-nth-1-las-to-pas

(defthm len-of-mv-nth-1-las-to-pas
  (implies (not (mv-nth 0 (las-to-pas n lin-addr r-w-x x86)))
           (equal (len (mv-nth 1 (las-to-pas n lin-addr r-w-x x86)))
                  (nfix n))))