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Symbolic-arithmetic

Bfr-logand-ss

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

Definitions and Theorems

Function: bfr-logand-ss

(defun bfr-logand-ss (a b)
  (declare (xargs :guard (and (true-listp a) (true-listp b))))
  (let ((__function__ 'bfr-logand-ss))
    (declare (ignorable __function__))
    (b* (((mv af ar aend) (first/rest/end a))
         ((when aend) (bfr-ite-bss af b '(nil)))
         ((mv bf br bend) (first/rest/end b))
         ((when bend) (bfr-ite-bss bf a '(nil)))
         (c (bfr-and af bf))
         (r (bfr-logand-ss ar br)))
      (bfr-scons c r))))

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

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

Theorem: bfr-logand-ss-correct

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

Theorem: bfr-logand-ss-deps

(defthm bfr-logand-ss-deps
  (b* ((a&b (bfr-logand-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 a&b))))))