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Symbolic-arithmetic

Bfr-floor-ss

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

Definitions and Theorems

Function: bfr-floor-ss

(defun bfr-floor-ss (a b)
 (declare (xargs :guard (and (true-listp a) (true-listp b))))
 (let ((__function__ 'bfr-floor-ss))
   (declare (ignorable __function__))
   (bfr-ite-bss (bfr-=-ss b nil)
                nil
                (b* (((mv bsign babs bneg)
                      (bfr-sign-abs-not-s b))
                     (anorm (bfr-ite-bss bsign (bfr-unary-minus-s a)
                                         a))
                     ((mv f &)
                      (bfr-floor-ss-aux anorm babs bneg)))
                  f))))

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

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

Theorem: bfr-floor-ss-correct

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

Theorem: bfr-floor-ss-deps

(defthm bfr-floor-ss-deps
  (b* ((f (bfr-floor-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 f))))))