feat(Topology/Algebra/Valued/LocallyCompact): locally compact nonarchimedean field iff complete and DVR and finite field

[pechersky]

---

• [x] depends on: #16731
• [x] depends on: #15777
• [ ] depends on: #16619
• [ ] depends on: #15424

[github-actions[bot]]

PR summary 01c4894bd3

Import changes exceeding 2%

%	File
+4.00%	Mathlib.Topology.Algebra.Valued.LocallyCompact

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Topology.Algebra.Valued.LocallyCompact	1574	1637	+63 (+4.00%)

Import changes for all files

Files	Import difference
Mathlib.Topology.Algebra.Valued.LocallyCompact	63

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Declarations diff

+ compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField + exists_nnnorm_lt_one + exists_norm_coe_lt_one + exists_norm_lt_one + isDiscreteValuationRing_of_compactSpace + isOpen_ball + isOpen_closedball + isOpen_sphere + isPrincipalIdealRing_of_compactSpace + properSpace_iff_compactSpace_integer + properSpace_iff_completeSpace_and_isDiscreteValuationRing_integer_and_finite_residueField

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:

• ~~leanprover-community/mathlib4#16731~~
• ~~leanprover-community/mathlib4#15777~~
• ~~leanprover-community/mathlib4#16619~~
• ~~leanprover-community/mathlib4#15424~~
• ~~leanprover-community/mathlib4#20373~~ By Dependent Issues (🤖). Happy coding!

[mathlib-bors[bot]]

:v: pechersky can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[pechersky]

bors r+

[mathlib-bors[bot]]

Pull request successfully merged into master.

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