@martinjuckes I'm fine with must as opposed to shall.

Regarding the logical structure, Here's how I see the logical structure of the 
paragraphs for dimension coordinate variables and auxiliary coordinate 
variables. (I'm using the first version.)

As logic statements:
* IF dimension coordinate variable THEN
   * has form "x(x)" AND
   * numeric type AND
   * strictly monotonic AND
   * no fill, etc
* IF NOT dimension coordinate variable THEN
   * NOT has form "x(x)"

The last statement could also be written as:
* IF NOT dimension coordinate variable AND has form "x(x)" THEN
   * ERROR

* IF auxiliary coordinate variable THEN
   *  NOT dimension coordinate variable
* IF auxiliary coordinate variable AND 1-D THEN
   * NOT have form "x(x)"

Again, the last statement could also be written as:
* IF auxiliary coordinate variable AND has form "x(x)" THEN
   * ERROR

As structured text:
* The coordinate variable concept is described.
* There are two types of coordinate variables:
   * Dimension coordinate variables:
      * A dimension coordinate variable must:
         * be a one-dimensional variable that has the same name as its dimension
         * have a numeric type
         * contain strictly monotonic values
         * not contain fill, missing, or out-of range values.
      * A one-dimensional variable that is not a dimension coordinate variable 
must not have the same name as its dimension.
   * Auxiliary coordinate variables:
      * An auxiliary coordinate variable must:
         * contain coordinate values that cannot be expressed in the form of a 
dimension coordinate variable
            * example provided
      * An auxiliary coordinate variable may:
         * have any number of dimensions
         * have non-numeric type
         * be non-monotonic
         * be non-unique
         * contain fill, etc
      * A one-dimensional auxiliary coordinate variable shall not have the same 
name as its dimension.

I was reminded of something while I was writing this comment. A data variable 
can fortuitously meet all the requirements for an auxiliary coordinate variable 
or (other than the form restriction) a dimension coordinate variable. An 
auxiliary coordinate variable can fortuitously meet all the requirements (other 
than the form restriction) for a dimension coordinate variable. Intention for a 
variable matters. It's not just a matter of having particular attributes.

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