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feat(analysis/analytic/composition): the composition of analytic func…
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…tions is analytic (#2399)

The composition of analytic functions is analytic. 
The argument is the following. Assume `g z = ∑ qₙ (z, ..., z)` and `f y = ∑ pₖ (y, ..., y)`. Then
```
g (f y) = ∑ qₙ (∑ pₖ (y, ..., y), ..., ∑ pₖ (y, ..., y))
= ∑ qₙ (p_{i₁} (y, ..., y), ..., p_{iₙ} (y, ..., y)).
```
For each `n` and `i₁, ..., iₙ`, define a `i₁ + ... + iₙ` multilinear function mapping
`(y₀, ..., y_{i₁ + ... + iₙ - 1})` to
`qₙ (p_{i₁} (y₀, ..., y_{i₁-1}), p_{i₂} (y_{i₁}, ..., y_{i₁ + i₂ - 1}), ..., p_{iₙ} (....)))`.
Then `g ∘ f` is obtained by summing all these multilinear functions.

The main difficulty is to make sense of this (especially the ellipsis) in a way that Lean understands. For this, this PR uses a structure containing a decomposition of `n` as a sum `i_1 + ... i_k` (called `composition`), and a whole interface around it developed in #2398. Once it is available, the main proof is not too hard.

This supersedes #2328, after a new start implementing compositions using sequences.

Co-authored-by: Scott Morrison <scott@tqft.net>
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sgouezel and semorrison committed Apr 17, 2020
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