 x&lt;j&gt; for j = 1 to k.

If you really want to try and pull a fast one,
you can change the second L to a L', and thus:

|   L(x&lt;1&gt;, ..., x&lt;k&gt;)
|
|   iff
|
|   There exists y such L'(y) and Proj&lt;j&gt;(y) = x&lt;j&gt; for j = 1 to k.

Voila!  Instant profundamento!

| Had Peirce or Whitehead lived a little longer maybe they would have
| become aware of the fact that any n-ary relation can be defined in
| terms of binary relations, with the aid of the existential quantifier.
| The translatio