DTV_ — Mischaracterized description of 'properly overlaps' in text

The description for "Properly overlaps" in this section is as follows:

"The ‘properly overlaps’ relation distinguishes the case in which there is a part of each time interval that is not a part the other from all the cases in which one time interval is entirely a part of the other. The general ‘overlaps’ relation subsumes all of them. ‘Properly overlaps’ describes the first time interval as starting and ending earlier than the second, whereas ‘is properly overlapped by’ describes the first time interval as starting and ending later."

Problem:

In the phrase "‘Properly overlaps’ describes the first time interval as starting and ending earlier than the second," the sense which is intended is in fact "‘Properly overlaps’ describes the first time interval as starting earlier than the second starts and ending earlier than the second ends"

That is, a word was left implied in this phrase, but no one word would, when inserted here, have carried the correct meaning. For example "starting and ending earlier than the second [starts]" would be incorrect, as would "starting and ending earlier than the second [ends]". So when the reader parses this surface-level syntax and inserts any implied words for a deeper level cognitive representation of the meaning, any such representation would be incorrect compared to the intended sense of this term.

Similarly in the phrase which follows:
"... whereas ‘is properly overlapped by’ describes the first time interval as starting and ending later."

should then (presumably) be:
"... whereas ‘is properly overlapped by’ describes the first time interval as starting later than the second starts, and ending later than the second ends."

Proposed Solution:
Rewrite the offending paragraph as follows:

"The ‘properly overlaps’ relation distinguishes the case in which there is a part of each time interval that is not a part the other from all the cases in which one time interval is entirely a part of the other. The general ‘overlaps’ relation subsumes all of them. ‘Properly overlaps’ describes the first time interval as starting earlier than the second starts and ending earlier than the second ends, whereas ‘is properly overlapped by’ describes the first time interval as starting later than the second starts, and ending later than the second ends."

Replace text as described below.