## outline

#### 1

In brief outline, here is the main idea of the proof.

In outline, the argument follows that of the single-valued setting, but there are several significant issues that must be addressed in the $n$-valued case.

The outline of this paper is as follows.

#### 2

We shall briefly outline the necessary changes.

Where it is possible, we outline the proofs so that the reader will not have to hunt for obscure references.

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