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Distance-to-tab

Signature
(distance-to-tab col tabsize) → *
Arguments: col — Guard (natp col).; tabsize — Guard (posp tabsize).

Definitions and Theorems

Function: distance-to-tab$inline

(defun distance-to-tab$inline (col tabsize)
  (declare (xargs :guard (and (natp col) (posp tabsize))))
  (declare (type unsigned-byte col tabsize))
  (declare (xargs :split-types t))
  (let ((acl2::__function__ 'distance-to-tab))
    (declare (ignorable acl2::__function__))
    (mbe :logic
         (b* ((col (nfix col))
              (tabsize (acl2::pos-fix tabsize)))
           (nfix (- tabsize (rem col tabsize))))
         :exec (- tabsize
                  (the unsigned-byte (rem col tabsize))))))

Theorem: distance-to-tab$inline-of-nfix-col

(defthm distance-to-tab$inline-of-nfix-col
  (equal (distance-to-tab$inline (nfix col)
                                 tabsize)
         (distance-to-tab$inline col tabsize)))

Theorem: distance-to-tab$inline-nat-equiv-congruence-on-col

(defthm distance-to-tab$inline-nat-equiv-congruence-on-col
  (implies (acl2::nat-equiv col col-equiv)
           (equal (distance-to-tab$inline col tabsize)
                  (distance-to-tab$inline col-equiv tabsize)))
  :rule-classes :congruence)

Theorem: distance-to-tab$inline-of-pos-fix-tabsize

(defthm distance-to-tab$inline-of-pos-fix-tabsize
  (equal (distance-to-tab$inline col (acl2::pos-fix tabsize))
         (distance-to-tab$inline col tabsize)))

Theorem: distance-to-tab$inline-pos-equiv-congruence-on-tabsize

(defthm distance-to-tab$inline-pos-equiv-congruence-on-tabsize
  (implies (acl2::pos-equiv tabsize tabsize-equiv)
           (equal (distance-to-tab$inline col tabsize)
                  (distance-to-tab$inline col tabsize-equiv)))
  :rule-classes :congruence)