feat(AlgebraicTopology/SimplexCategory/GeneratorsRelations/NormalForms): Normal forms for P_δs

[robin-carlier]

We prove that admissible lists indeed provide a normal form for morphisms of satisfying P_δ.
To this end, we introduce standardδ, a construction that takes a list and turn it into a composition of δ is in SimplexCategoryGenRel. We then prove that, thanks to the first simplicial identity, composition on the left corresponds to simplicial insertion in the list. This gives existence of a normal form for every morphism satisfying P_δ.

For unicity, we introduce an auxiliary function simplicialEvalδ : (List ℕ) → ℕ → ℕ and show that for admissible lists, it lifts to ℕ the orderHom attached to toSimplexCategory.map standardδ, and that we can recover elements of the list only by looking at values of this function.

Part of a series of PR formalising that SimplexCategoryGenRel is equivalent to SimplexCategory.

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• depends on: [Merged by Bors] - feat(AlgebraicTopology/SimplexCategory/GeneratorsRelations/NormalForms): Normal forms for P_σs #25736

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This PR continues the work from #21746.

Original PR: #21746

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - feat(AlgebraicTopology/SimplexCategory/GeneratorsRelations/NormalForms): Normal forms for P_σs #25736
  By Dependent Issues (🤖). Happy coding!

[joelriou]

Thanks!

bors d+

[mathlib-bors]

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