refactor(PiTensorProduct/{InjectiveNorm, ProjectiveNorm}): switch NormedSpace instance to projectiveSeminorm

[goliath-klein]

We switch the NormedSpace instance on PiTensorProducts from injectiveSeminorm to projectiveSeminorm and update all follow-up results.

The signature of norm_eval_le_projectiveSeminorm is changed to match the one of norm_eval_le_injectiveSeminorm.

This is the second in a series of three PRs with the goal to deprecate PiTensorProuduct.injectiveSeminorm.

---

• depends on: refactor(PiTensorProduct/{InjectiveNorm, ProjectiveNorm}): Golfs #35567

Co-authored-by: Davood H. H. Tehrani

[github-actions]

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[github-actions]

PR summary d6f48e471c

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ instance (x : ⨂[R] i, s i) : Nonempty ↑x.lifts := nonempty_subtype.mpr (nonempty_lifts x)
+ instance : Norm (⨂[𝕜] i, E i)
+ instance : NormedSpace 𝕜 (⨂[𝕜] i, E i) := ⟨projectiveSeminorm_smul_le⟩
+ norm_def
+ projectiveSeminorm_add_le
+ projectiveSeminorm_smul_le
+ projectiveSeminorm_zero
- instance : NormedSpace 𝕜 (⨂[𝕜] i, E i)
- projectiveSeminorm_apply

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 scripts/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).

[mathlib-dependent-issues]

This PR/issue depends on:

• refactor(PiTensorProduct/{InjectiveNorm, ProjectiveNorm}): Golfs #35567
  By Dependent Issues (🤖). Happy coding!