feat(Algebra/Colimit): the directed system of finitely generated submodules

[alreadydone]

We show that every module is the direct limit of its finitely generated submodules.

As a consequence of this and the fact that tensor products preserves colimits, we show that if M and P are arbitrary modules and N is a finitely generated submodule of a module P, then two elements of N ⊗ M have the same image in P ⊗ M if and only if they already have the same image in N' ⊗ M for some finitely generated submodule N' ≥ N. This is the theorem Submodule.FG.exists_rTensor_fg_inclusion_eq.

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[github-actions]

PR summary 05c988734b

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Algebra.Colimit.Finiteness (new file)	977

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Declarations diff

+ Submodule.FG.exists_rTensor_fg_inclusion_eq
+ directLimitLeft_rTensor_of
+ equiv
+ equiv_comp_of
+ exists_eq_of_of_eq
+ fgSystem
+ instance : DirectedSystem (G · ⊗[R] M) (f ▷ M)
+ instance : DirectedSystem (M ⊗[R] G ·) (M ◁ f)
+ instance : DirectedSystem _ (fgSystem R M · · · ·)
+ instance : IsDirected {N : Submodule R M // N.FG} (· ≤ ·)

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.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).