feat(Valued/LocallyCompact): `totallyBounded_iff_finite_residueField`

[pechersky]

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• [x] depends on: #14768
• [x] depends on: #15425
• [ ] depends on: #15426
• [ ] depends on: #17561

[github-actions[bot]]

PR summary 7249957d74

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Topology.Algebra.Valued.LocallyCompact (new file)	1463

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Declarations diff

+ NormedField.v_eq_valuation + _root_.Irreducible.maximalIdeal_eq_closedBall + _root_.Irreducible.maximalIdeal_pow_eq_closedBall_pow + coe_span_singleton_eq_closedBall + finite_quotient_maximalIdeal_pow_of_finite_residueField + isUnit_iff_norm_eq_one + mem_iff + norm_coe_unit + norm_irreducible_lt_one + norm_irreducible_pos + norm_le_one + norm_unit + totallyBounded_iff_finite_residueField + valuation_unit

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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#14768~~
• ~~leanprover-community/mathlib4#15425~~
• ~~leanprover-community/mathlib4#15426~~
• ~~leanprover-community/mathlib4#17561~~ By Dependent Issues (🤖). Happy coding!

[mathlib-bors[bot]]

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