feat: combinatorial part of the Faa di Bruno formula

[sgouezel]

The Faa di Bruno formula expresses D^n (g o f) in terms of the iterated derivatives of g and f. The hardest part of the formalization is probably just being able to express the formula. This PR deals with the combinatorial prerequisites for the proof of the formula, defining ordered finpartitions of Fin n and showing how an ordered finpartition of Fin (n+1) can be built out of an ordered finpartition of Fin n.

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[github-actions]

PR summary de6e9ca8fc

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno	742

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Declarations diff

+ OrderedFinpartition
+ atomic
+ embSigma
+ emb_injective
+ emb_invEmbedding
+ emb_ne_emb_of_ne
+ emb_zero
+ equivSigma
+ eraseLeft
+ eraseMiddle
+ exists_inverse
+ extend
+ extendEquiv
+ extendLeft
+ extendMiddle
+ index
+ index_extendMiddle_zero
+ injective_embSigma
+ instance : Fintype (OrderedFinpartition n)
+ instance : Inhabited (OrderedFinpartition n) := ⟨atomic n⟩
+ instance : Unique (OrderedFinpartition 0) := by
+ invEmbedding
+ length_le
+ length_pos
+ neZero_length
+ neZero_partSize
+ one_lt_partSize_index_zero
+ partSize_eq_one_of_range_emb_eq_singleton
+ partSize_le
+ prod_sigma_eq_prod
+ range_extendLeft_zero
+ range_extendMiddle_emb_ne_singleton_zero
+ to

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.