feat(RingTheory/LocalProperties): being projective can be checked locally on stalks

[erdOne]

... for finitely presented modules

Written at the AIM algebraic geometry workshop

Co-authored-by: David Swinarski

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• depends on: [Merged by Bors] - feat(RingTheory/*): prerequisites to the locality of projectivity #18264

[github-actions]

PR summary cc2212a3c7

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RingTheory.LocalProperties.Submodule	1188
Mathlib.RingTheory.LocalProperties.Projective	1207

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Declarations diff

+ LinearMap.split_surjective_of_localization_maximal
+ Module.eq_of_localization_maximal
+ Module.eq_zero_of_localization_maximal
+ Module.projective_of_isLocalizedModule
+ Module.projective_of_localization_maximal
+ Module.projective_of_localization_maximal'
+ Module.subsingleton_of_localization_maximal
+ Submodule.eq_bot_of_localization_maximal
+ Submodule.eq_of_localization_maximal
+ Submodule.le_of_localization_maximal
+ Submodule.mem_of_localization_maximal
+ instance [Module.FinitePresentation R M] :

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.

[erdOne]

Thanks for the review!

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - feat(RingTheory/*): prerequisites to the locality of projectivity #18264
  By Dependent Issues (🤖). Happy coding!