		Search-engine friendly clone of the ACL2 documentation.

Symbolic-arithmetic

Bfr-rem-ss

Signature
(bfr-rem-ss a b) → r
Arguments: a — Guard (true-listp a).; b — Guard (true-listp b).
Returns: r — Type (true-listp r).

Definitions and Theorems

Function: bfr-rem-ss

(defun bfr-rem-ss (a b)
  (declare (xargs :guard (and (true-listp a) (true-listp b))))
  (let ((__function__ 'bfr-rem-ss))
    (declare (ignorable __function__))
    (bfr-ite-bss
         (bfr-=-ss b nil)
         (llist-fix a)
         (b* (((mv & babs bneg)
               (bfr-sign-abs-not-s b))
              ((mv asign aabs &)
               (bfr-sign-abs-not-s a))
              (m (bfr-mod-ss-aux aabs babs bneg)))
           (bfr-logext-ns (integer-length-bound-s b)
                          (bfr-ite-bss asign (bfr-unary-minus-s m)
                                       m))))))

Theorem: true-listp-of-bfr-rem-ss

(defthm true-listp-of-bfr-rem-ss
  (b* ((r (bfr-rem-ss a b)))
    (true-listp r))
  :rule-classes :type-prescription)

Theorem: bfr-rem-ss-correct

(defthm bfr-rem-ss-correct
  (b* ((r (bfr-rem-ss a b)))
    (and (equal (bfr-list->s r env)
                (rem (bfr-list->s a env)
                     (bfr-list->s b env))))))

Theorem: bfr-rem-ss-deps

(defthm bfr-rem-ss-deps
  (b* ((r (bfr-rem-ss a b)))
    (implies (and (not (pbfr-list-depends-on varname param a))
                  (not (pbfr-list-depends-on varname param b)))
             (and (not (pbfr-list-depends-on varname param r))))))