File: rom-helpers.lisp

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acl2 8.6%2Bdfsg-3
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(in-package "ACL2")

(defund bvecp (x k)
  (declare (xargs :guard (integerp k)))
  (and (integerp x)
       (<= 0 x)
       (< x (expt 2 k))))
(local (in-theory (enable bvecp)))

(local ; ACL2 primitive
 (defun natp (x)
   (declare (xargs :guard t))
   (and (integerp x)
        (<= 0 x))))

(defun check-array (name a dim1 dim2)
  (if (zp dim1)
      t
    (and (bvecp (aref1 name a (1- dim1)) dim2)
	 (check-array name a (1- dim1) dim2))))

(defthm check-array-lemma-1
    (implies (and (not (zp dim1))
		  (check-array name a dim1 dim2)
		  (natp i)
		  (< i dim1))
	     (bvecp (aref1 name a i) dim2))
  :rule-classes ())

(defthm check-array-lemma
    (implies (and (bvecp i n)
		  (not (zp (expt 2 n)))
		  (check-array name a (expt 2 n) dim2))
	     (bvecp (aref1 name a i) dim2))
  :rule-classes ()
  :hints (("Goal" :use ((:instance check-array-lemma-1 (dim1 (expt 2 n)))))))