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Symbolic-arithmetic

Aabf-truncate-ss

Signature
(aabf-truncate-ss a b man) → (mv tr new-man)
Arguments: a — Guard (true-listp a).; b — Guard (true-listp b).

Definitions and Theorems

Function: aabf-truncate-ss

(defun aabf-truncate-ss (a b man)
  (declare (xargs :guard (and (true-listp a) (true-listp b))))
  (declare (xargs :guard (and (aabflist-p a man)
                              (aabflist-p b man))))
  (let ((__function__ 'aabf-truncate-ss))
    (declare (ignorable __function__))
    (b* (((mv zero man) (aabf-=-ss b nil man))
         ((when (aabf-syntactically-true-p zero man))
          (mv nil man))
         ((mv bsign babs bneg man)
          (aabf-sign-abs-not-s b man))
         ((mv asign aabs & man)
          (aabf-sign-abs-not-s a man))
         ((mv f & man)
          (aabf-floor-ss-aux aabs babs bneg man)))
      (aabf-nest (aabf-ite-bss zero nil
                               (aabf-ite-bss (aabf-xor bsign asign)
                                             (aabf-unary-minus-s f)
                                             f))
                 man))))

Theorem: trivial-theorem-about-aabf-truncate-ss

(defthm trivial-theorem-about-aabf-truncate-ss
  (b* nil
    (b* ((?ignore (aabf-truncate-ss a b man)))
      t))
  :rule-classes nil)

Theorem: true-listp-of-aabf-truncate-ss.tr

(defthm true-listp-of-aabf-truncate-ss.tr
  (b* (((mv ?tr ?new-man)
        (aabf-truncate-ss a b man)))
    (true-listp tr))
  :rule-classes :type-prescription)

Theorem: aabf-extension-p-of-aabf-truncate-ss

(defthm aabf-extension-p-of-aabf-truncate-ss
  (b* (((mv ?tr ?new-man)
        (aabf-truncate-ss a b man)))
    (aabf-extension-p new-man man)))

Theorem: aabf-p-of-aabf-truncate-ss

(defthm aabf-p-of-aabf-truncate-ss
  (b* (((mv tr new-man)
        (aabf-truncate-ss a b man)))
    (implies (and (aabflist-p a man)
                  (aabflist-p b man))
             (and (aabflist-p tr new-man)))))

Theorem: aabf-eval-of-aabf-truncate-ss

(defthm aabf-eval-of-aabf-truncate-ss
 (b* (((mv tr new-man)
       (aabf-truncate-ss a b man)))
  (implies
   (and (aabflist-p a man)
        (aabflist-p b man))
   (and
       (equal (bools->int (aabflist-eval tr env new-man))
              (truncate (bools->int (aabflist-eval a env man))
                        (bools->int (aabflist-eval b env man))))))))

Theorem: aabf-pred-of-aabf-truncate-ss

(defthm aabf-pred-of-aabf-truncate-ss
  (b* (((mv tr new-man)
        (aabf-truncate-ss a b man)))
    (implies (and (aabflist-p a man)
                  (aabflist-p b man)
                  (aabflist-pred a man)
                  (aabflist-pred b man))
             (and (aabflist-pred tr new-man)))))