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To illustrate, let us state the following corollary.
That (2) implies (1) is the content of Corollary 3.
This corollary calls for some explanation and comment.
The rest of the proof goes through as for Corollary 2, with hardly any changes.
The significance of this fact for our purposes is captured by Corollary 3.
We will finish this section by offering a second application of our machinery (although in truth it is largely a corollary of the above).
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