feat(Analysis/LocallyConvex): induction principles for WithSeminorm

[mcdoll]

Adds two "induction principles" for seminorms: a property holds for a continuous seminorm if it holds for all seminorms that induce the topology, the zero seminorm, is monotone, and closed under taking suprema and scalar multiplication.

We add two versions: one where we checked suprema and one where we check addition (the later being more convenient in practice).

Co-authored-by: Anatole Dedecker anatolededecker@gmail.com

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[github-actions]

PR summary 94e3baed03

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 (regex)

+ bound_sum_of_continuous
+ induction_add_of_continuous
+ induction_sup_of_continuous

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 94e3bae).

• +3 new declarations
• −0 removed declarations

+Seminorm.bound_sum_of_continuous
+Seminorm.induction_add_of_continuous
+Seminorm.induction_sup_of_continuous

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 94e3baed03
Reference commit 1abef63231

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/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).