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Bitarr-range-set

Signature

(bitarr-range-set start count bitarr) → *

Arguments

start — Guard (natp start).

count — Guard (natp count).

Definitions and Theorems

Function: bitarr-range-set

(defun bitarr-range-set (start count bitarr)
  (declare (xargs :stobjs (bitarr)))
  (declare (xargs :guard (and (natp start) (natp count))))
  (declare (xargs :guard (<= (+ start count)
                             (bits-length bitarr))))
  (let ((__function__ 'bitarr-range-set))
    (declare (ignorable __function__))
    (if (zp count)
        t
      (and (eql 1 (get-bit start bitarr))
           (bitarr-range-set (1+ (lnfix start))
                             (1- count)
                             bitarr)))))

Theorem: bitarr-range-set-implies-nth

(defthm bitarr-range-set-implies-nth
  (implies (and (bitarr-range-set start count bitarr)
                (<= (nfix start) (nfix n))
                (< (nfix n)
                   (+ (nfix start) (nfix count))))
           (equal (nth n bitarr) 1)))

Theorem: bitarr-range-set-of-update

(defthm bitarr-range-set-of-update
 (implies (and (equal idx (+ -1 (nfix start) count))
               (bitarr-range-set start (1- count)
                                 bitarr)
               (posp count))
          (bitarr-range-set start count (update-nth idx 1 bitarr))))

Theorem: bitarr-range-count-when-bitarr-range-set

(defthm bitarr-range-count-when-bitarr-range-set
  (implies (bitarr-range-set start count bitarr)
           (equal (bitarr-range-count start count bitarr)
                  (nfix count))))

Theorem: bitarr-range-set-of-nfix-start

(defthm bitarr-range-set-of-nfix-start
  (equal (bitarr-range-set (nfix start)
                           count bitarr)
         (bitarr-range-set start count bitarr)))

Theorem: bitarr-range-set-nat-equiv-congruence-on-start

(defthm bitarr-range-set-nat-equiv-congruence-on-start
  (implies (nat-equiv start start-equiv)
           (equal (bitarr-range-set start count bitarr)
                  (bitarr-range-set start-equiv count bitarr)))
  :rule-classes :congruence)

Theorem: bitarr-range-set-of-nfix-count

(defthm bitarr-range-set-of-nfix-count
  (equal (bitarr-range-set start (nfix count)
                           bitarr)
         (bitarr-range-set start count bitarr)))

Theorem: bitarr-range-set-nat-equiv-congruence-on-count

(defthm bitarr-range-set-nat-equiv-congruence-on-count
  (implies (nat-equiv count count-equiv)
           (equal (bitarr-range-set start count bitarr)
                  (bitarr-range-set start count-equiv bitarr)))
  :rule-classes :congruence)