feat(FieldTheory/Galois): Fundamental theorem of infinite galois theory

[Thmoas-Guan]

Prove the Fundamental theorem of infinite galois theory

---

• depends on: [Merged by Bors] - feat(Topology/Group): define closed subgroup #16977
• depends on: [Merged by Bors] - feat(FieldTheory/Galois): Finite galois subextensions #16978
• depends on: [Merged by Bors] - feat(FieldTheory/Galois): Lemmas of galois theory #16979
• depends on: [Merged by Bors] - chore(FieldTheory/Galois): Move infinite Galois #17945

[github-actions]

PR summary bd0c8d6807

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.FieldTheory.Galois.Infinite (new file)	1572

---

Declarations diff

+ GaloisCoinsertionIntermediateFieldSubgroup
+ GaloisInsertionIntermediateFieldSubgroup
+ IntermediateFieldEquivClosedSubgroup
+ finiteDimensional_of_le
+ fixedField_bot
+ fixedField_fixingSubgroup
+ fixingSubgroup_fixedField
+ fixingSubgroup_isClosed
+ instance : TopologicalSpace (K ≃ₐ[k] K) := inferInstance
+ mem_fixedField_iff
+ normal_iff_isGalois
+ open_iff_finite
+ restrict_fixedField

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.

---

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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - feat(Topology/Group): define closed subgroup #16977
• [Merged by Bors] - feat(FieldTheory/Galois): Finite galois subextensions #16978
• [Merged by Bors] - feat(FieldTheory/Galois): Lemmas of galois theory #16979
• [Merged by Bors] - chore(FieldTheory/Galois): Move infinite Galois #17945
  By Dependent Issues (🤖). Happy coding!