chore(Analysis/InnerProductSpace/TensorProduct): remove private inner_ definition

[themathqueen]

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[github-actions]

PR summary e4dde51dfe

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)

- inner_

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 e4dde51).

• +1 new declarations
• −0 removed declarations

+TensorProduct.inner_def

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Decrease in strong tech debt: (relative, absolute) = (1.34, 0.01)

Current number	Change	Type (strong)
730	-2	backward.privateInPublic
384	-1	backward.privateInPublic.warn

No changes to weak technical debt.

Current commit e4dde51dfe
Reference commit b33266fe41

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).