feat: Refactor and add some easy lemmas about Galois theory

[yhtq]

Move fixingSubgroup_top/bot back to Galois.basic, add fixedField_top/bot,mem_bot_iff_fixed and mem_range_algebraMap_iff_fixed

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[github-actions]

PR summary 324a7e0be1

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ fixedField_bot
+ fixedField_top
+ fixingSubgroup_bot
+ fixingSubgroup_top
+ mem_bot_iff_fixed
+ mem_fixingSubgroup_iff
+ mem_range_algebraMap_iff_fixed
- IntermediateField.fixingSubgroup_bot
- IntermediateField.fixingSubgroup_top
- IntermediateField.mem_fixingSubgroup_iff

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).

[tb65536]

Note that this PR overlaps with #22971

[Thmoas-Guan]

@yhtq @mbkybky shall we are combining this one with #22971? So we are merging that one into this PR and close #22971,right?

[adomani]

I wonder whether the _root_ here is an indication that the namespaced mem_fixingSubgroup_iff should be protected instead.

[yhtq]

@yhtq @mbkybky shall we are combining this one with #22971? So we are merging that one into this PR and close #22971,right?

I think #22971 makes a little more changes than me. So perhaps merging this PR into that one and close this one?

[mbkybky]

I think #22971 makes a little more changes than me. So perhaps merging this PR into that one and close this one?

Ok, I think it's fine.