The optimist's theorem says that if we can decompose a problem
into a downward-closed bit **P** and the rest (not necessarily
downward-closed) **Q**, then we may perform relative optimisation
in sequence, reducing the accumulated bound *b* to some
*f* which maximises **P**, then maximising **Q** relative
to *f*. Effectively, we reduce the **P** component of
the constraint to bounding by *f*.

Decomposing the hypotheses and the conclusion, we acquire or require three things each:

- satisfaction of the property
- bounding by the accumulator
- optimality of the solution

You can tell this is an abstract slide, because it's all green and blue, not red and purple.

Let's complete the proof.

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