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All-xlation-governing-entries-paddrs

Signature

(all-xlation-governing-entries-paddrs n lin-addr x86) → *

Arguments

n — Guard (natp n).

lin-addr — Guard (canonical-address-p lin-addr).

Definitions and Theorems

Function: all-xlation-governing-entries-paddrs

(defun all-xlation-governing-entries-paddrs (n lin-addr x86)
 (declare (xargs :stobjs (x86)))
 (declare (xargs :guard (and (natp n)
                             (canonical-address-p lin-addr))))
 (declare (xargs :guard (and (not (app-view x86))
                             (canonical-address-p (+ n lin-addr)))))
 (let ((__function__ 'all-xlation-governing-entries-paddrs))
   (declare (ignorable __function__))
   (if (zp n)
       nil
     (append (xlation-governing-entries-paddrs lin-addr x86)
             (all-xlation-governing-entries-paddrs (1- n)
                                                   (1+ lin-addr)
                                                   x86)))))

Theorem: all-xlation-governing-entries-paddrs-and-zero-bytes

(defthm all-xlation-governing-entries-paddrs-and-zero-bytes
  (equal (all-xlation-governing-entries-paddrs 0 lin-addr x86)
         nil))

Theorem: xlation-governing-entries-paddrs-subset-p-all-xlation-governing-entries-paddrs

(defthm
 xlation-governing-entries-paddrs-subset-p-all-xlation-governing-entries-paddrs
 (implies
   (and (<= addr a)
        (< a (+ n addr))
        (posp n)
        (integerp a)
        (integerp addr))
   (equal
        (subset-p (xlation-governing-entries-paddrs a x86)
                  (all-xlation-governing-entries-paddrs n addr x86))
        t)))

Theorem: all-xlation-governing-entries-paddrs-subset-p-all-xlation-governing-entries-paddrs

(defthm
 all-xlation-governing-entries-paddrs-subset-p-all-xlation-governing-entries-paddrs
 (implies
  (and (<= addr-2 addr-1)
       (<= (+ n-1 addr-1) (+ n-2 addr-2))
       (posp n-2)
       (integerp addr-1)
       (integerp addr-2))
  (equal
    (subset-p (all-xlation-governing-entries-paddrs n-1 addr-1 x86)
              (all-xlation-governing-entries-paddrs n-2 addr-2 x86))
    t)))

Theorem: all-xlation-governing-entries-paddrs-and-xw-not-mem

(defthm all-xlation-governing-entries-paddrs-and-xw-not-mem
  (implies (and (not (equal fld :mem))
                (not (equal fld :ctr))
                (not (equal fld :app-view)))
           (equal (all-xlation-governing-entries-paddrs
                       n addr (xw fld index value x86))
                  (all-xlation-governing-entries-paddrs
                       n addr (double-rewrite x86)))))

Theorem: all-xlation-governing-entries-paddrs-and-xw-mem-not-member

(defthm all-xlation-governing-entries-paddrs-and-xw-mem-not-member
  (implies (not (member-p index
                          (all-xlation-governing-entries-paddrs
                               n addr (double-rewrite x86))))
           (equal (all-xlation-governing-entries-paddrs
                       n addr (xw :mem index value x86))
                  (all-xlation-governing-entries-paddrs
                       n addr (double-rewrite x86)))))