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Col-after-nthcdr

Determine what the new column number should be after we advance n characters.

Signature

(col-after-nthcdr n x col) → new-col

Arguments

n — How many characters to cdr.
    Guard (natp n).

x — Characters we're processing.
    Guard (character-listp x).

col — Current column number.
    Guard (natp col).

Returns

new-col — Type (natp new-col).

This is a logically simple way to express how the column number gets updated. It isn't really meant to be executed.

Definitions and Theorems

Function: col-after-nthcdr

(defun col-after-nthcdr (n x col)
  (declare (xargs :guard (and (natp n)
                              (character-listp x)
                              (natp col))))
  (let ((__function__ 'col-after-nthcdr))
    (declare (ignorable __function__))
    (if (or (zp n) (atom x))
        (lnfix col)
      (col-after-nthcdr (- n 1)
                        (cdr x)
                        (if (eql (car x) #\Newline)
                            0
                          (+ 1 (lnfix col)))))))

Theorem: natp-of-col-after-nthcdr

(defthm natp-of-col-after-nthcdr
  (b* ((new-col (col-after-nthcdr n x col)))
    (natp new-col))
  :rule-classes :type-prescription)

Theorem: nat-equiv-implies-equal-col-after-nthcdr-1

(defthm nat-equiv-implies-equal-col-after-nthcdr-1
  (implies (nat-equiv n n-equiv)
           (equal (col-after-nthcdr n x col)
                  (col-after-nthcdr n-equiv x col)))
  :rule-classes (:congruence))

Theorem: nat-equiv-implies-equal-col-after-nthcdr-3

(defthm nat-equiv-implies-equal-col-after-nthcdr-3
  (implies (nat-equiv col col-equiv)
           (equal (col-after-nthcdr n x col)
                  (col-after-nthcdr n x col-equiv)))
  :rule-classes (:congruence))

Theorem: upper-bound-1-of-col-after-nthcdr

(defthm upper-bound-1-of-col-after-nthcdr
  (<= (col-after-nthcdr n x col)
      (+ (nfix col) (nfix n)))
  :rule-classes ((:rewrite) (:linear)))

Theorem: upper-bound-2-of-col-after-nthcdr

(defthm upper-bound-2-of-col-after-nthcdr
  (<= (col-after-nthcdr n x col)
      (+ (nfix col) (len x)))
  :rule-classes ((:rewrite) (:linear)))