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• All-mem-except-paging-structures-equal

All-mem-except-paging-structures-equal-aux

Signature

(all-mem-except-paging-structures-equal-aux 
     i paging-qword-addresses x86-1 x86-2) 
 
  → 
*

Definitions and Theorems

Function: all-mem-except-paging-structures-equal-aux

(defun all-mem-except-paging-structures-equal-aux
       (i paging-qword-addresses x86-1 x86-2)
 (declare
  (xargs
       :non-executable t
       :guard (and (natp i)
                   (<= i *mem-size-in-bytes*)
                   (mult-8-qword-paddr-listp paging-qword-addresses)
                   (x86p x86-1)
                   (x86p x86-2))))
 (prog2$
  (acl2::throw-nonexec-error
       'all-mem-except-paging-structures-equal-aux
       (list i paging-qword-addresses x86-1 x86-2))
  (let ((__function__ 'all-mem-except-paging-structures-equal-aux))
    (declare (ignorable __function__))
    (if
     (zp i)
     (if (disjoint-p (list i)
                     (open-qword-paddr-list paging-qword-addresses))
         (equal (xr :mem i x86-1)
                (xr :mem i x86-2))
       t)
     (if (disjoint-p (list (1- i))
                     (open-qword-paddr-list paging-qword-addresses))
         (and (equal (xr :mem (1- i) x86-1)
                     (xr :mem (1- i) x86-2))
              (all-mem-except-paging-structures-equal-aux
                   (1- i)
                   paging-qword-addresses x86-1 x86-2))
       (all-mem-except-paging-structures-equal-aux
            (1- i)
            paging-qword-addresses x86-1 x86-2))))))

Theorem: all-mem-except-paging-structures-equal-aux-and-xr-mem-from-rest-of-memory

(defthm
 all-mem-except-paging-structures-equal-aux-and-xr-mem-from-rest-of-memory
 (implies
  (and
    (all-mem-except-paging-structures-equal-aux i addrs x86-1 x86-2)
    (disjoint-p (list j)
                (open-qword-paddr-list addrs))
    (natp i)
    (natp j)
    (< j i))
  (equal (xr :mem j x86-1)
         (xr :mem j x86-2))))

Theorem: all-mem-except-paging-structures-equal-aux-and-rm-low-32-from-rest-of-memory

(defthm
 all-mem-except-paging-structures-equal-aux-and-rm-low-32-from-rest-of-memory
 (implies
  (and
    (all-mem-except-paging-structures-equal-aux i addrs x86-1 x86-2)
    (disjoint-p (addr-range 4 j)
                (open-qword-paddr-list addrs))
    (natp i)
    (natp j)
    (< (+ 3 j) i)
    (not (app-view x86-1))
    (not (app-view x86-2)))
  (equal (rm-low-32 j x86-1)
         (rm-low-32 j x86-2))))

Theorem: all-mem-except-paging-structures-equal-aux-and-rm-low-64-from-rest-of-memory

(defthm
 all-mem-except-paging-structures-equal-aux-and-rm-low-64-from-rest-of-memory
 (implies
  (and
    (all-mem-except-paging-structures-equal-aux i addrs x86-1 x86-2)
    (disjoint-p (addr-range 8 j)
                (open-qword-paddr-list addrs))
    (natp i)
    (natp j)
    (< (+ 7 j) i)
    (not (app-view x86-1))
    (not (app-view x86-2)))
  (equal (rm-low-64 j x86-1)
         (rm-low-64 j x86-2))))

Theorem: all-mem-except-paging-structures-equal-aux-is-reflexive

(defthm all-mem-except-paging-structures-equal-aux-is-reflexive
  (all-mem-except-paging-structures-equal-aux i addrs x x))

Theorem: all-mem-except-paging-structures-equal-aux-is-commutative

(defthm all-mem-except-paging-structures-equal-aux-is-commutative
 (implies (all-mem-except-paging-structures-equal-aux i addrs x y)
          (all-mem-except-paging-structures-equal-aux i addrs y x)))

Theorem: all-mem-except-paging-structures-equal-aux-is-transitive

(defthm all-mem-except-paging-structures-equal-aux-is-transitive
 (implies
      (and (all-mem-except-paging-structures-equal-aux i addrs x y)
           (all-mem-except-paging-structures-equal-aux i addrs y z))
      (all-mem-except-paging-structures-equal-aux i addrs x z)))

Theorem: all-mem-except-paging-structures-equal-aux-and-xw-1

(defthm all-mem-except-paging-structures-equal-aux-and-xw-1
 (implies
  (not (equal fld :mem))
  (equal (all-mem-except-paging-structures-equal-aux
              i addrs (xw fld index val x)
              y)
         (all-mem-except-paging-structures-equal-aux i addrs x y))))

Theorem: all-mem-except-paging-structures-equal-aux-and-xw-2

(defthm all-mem-except-paging-structures-equal-aux-and-xw-2
 (implies
  (not (equal fld :mem))
  (equal (all-mem-except-paging-structures-equal-aux
              i addrs x (xw fld index val y))
         (all-mem-except-paging-structures-equal-aux i addrs x y))))

Theorem: all-mem-except-paging-structures-equal-aux-and-xw-mem

(defthm all-mem-except-paging-structures-equal-aux-and-xw-mem
  (implies (all-mem-except-paging-structures-equal-aux i addrs x y)
           (all-mem-except-paging-structures-equal-aux
                i addrs (xw :mem index val x)
                (xw :mem index val y))))

Theorem: xr-mem-wm-low-64

(defthm xr-mem-wm-low-64
  (implies (not (member-p index (addr-range 8 addr)))
           (equal (xr :mem index (wm-low-64 addr val x86))
                  (xr :mem index x86))))

Theorem: all-mem-except-paging-structures-equal-aux-and-wm-low-64-paging-entry

(defthm
 all-mem-except-paging-structures-equal-aux-and-wm-low-64-paging-entry
 (implies
  (member-p index addrs)
  (equal (all-mem-except-paging-structures-equal-aux
              i addrs (wm-low-64 index val x)
              y)
         (all-mem-except-paging-structures-equal-aux i addrs x y))))

Theorem: all-mem-except-paging-structures-equal-aux-and-wm-low-64

(defthm all-mem-except-paging-structures-equal-aux-and-wm-low-64
  (implies
       (and (all-mem-except-paging-structures-equal-aux i addrs x y)
            (not (xr :app-view nil x))
            (not (xr :app-view nil y)))
       (all-mem-except-paging-structures-equal-aux
            i addrs (wm-low-64 index val x)
            (wm-low-64 index val y))))

Theorem: all-mem-except-paging-structures-equal-aux-and-xw-mem-commute-writes

(defthm
 all-mem-except-paging-structures-equal-aux-and-xw-mem-commute-writes
 (implies (not (equal index-1 index-2))
          (all-mem-except-paging-structures-equal-aux
               i addrs
               (xw :mem
                   index-1 val-1 (xw :mem index-2 val-2 x))
               (xw :mem index-2
                   val-2 (xw :mem index-1 val-1 x)))))