feat: differentiation of test function as a CLM

[ADedecker]

Co-authored-by: @luigi-massacci

---

• depends on: feat: endow test functions with the natural LF topology #31806

[github-actions]

PR summary 082440f5b2

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ coe_mk
+ continuous_iff_continuous_comp
+ continuous_ofSupportedIn
+ fderivLM_ofSupportedIn
+ fderivWithOrderLM_ofSupportedIn
+ instance : ContinuousSMul ℝ 𝓓^{n}(Ω, F) := by
+ instance : IsTopologicalAddGroup 𝓓^{n}(Ω, F) := by
+ instance : LocallyConvexSpace ℝ 𝓓^{n}(Ω, F) := by
+ iteratedFDeriv_zero_on_compl
+ norm_apply_le_seminorm
+ norm_iteratedFDeriv_apply_le
+ norm_iteratedFDeriv_apply_le_seminorm
+ norm_iteratedFDeriv_apply_le_seminorm_withOrder
+ norm_iteratedFDeriv_apply_le_withOrder
+ norm_toBoundedContinuousFunction
+ ofSupportedIn
+ ofSupportedInCLM
+ ofSupportedInCLM_apply
+ ofSupportedInLM
+ ofSupportedInLM_apply
+ originalTop
+ originalTop_le
+ postcompCLM
+ postcompCLM_apply
+ postcompLM
+ postcompLM_apply
+ seminorm
+ seminorm'
+ seminorm_apply
+ seminorm_eq_bot_of_gt
+ seminorm_fderivLM
+ seminorm_fderivWithOrderLM_le
+ seminorm_le_iff
+ seminorm_le_iff_withOrder
+ seminorm_postcompLM_le
+ toBoundedContinuousFunctionCLM
+ toBoundedContinuousFunctionCLM_apply
+ toBoundedContinuousFunctionCLM_eq_of_scalars
+ topologicalSpace
+ topologicalSpace_le_iff
+ withSeminorms
+ withSeminorms'
++ fderivCLM
++ fderivCLM_apply
++ fderivCLM_eq_of_scalars
++ fderivCLM_eq_withOrder
++ fderivLM
++ fderivLM_apply
++ fderivLM_eq_of_scalars
++ fderivLM_eq_withOrder
++ fderivWithOrderCLM
++ fderivWithOrderCLM_apply
++ fderivWithOrderCLM_apply_of_gt
++ fderivWithOrderCLM_apply_of_le
++ fderivWithOrderCLM_eq_of_scalars
++ fderivWithOrderLM
++ fderivWithOrderLM_apply
++ fderivWithOrderLM_apply_of_gt
++ fderivWithOrderLM_apply_of_le
++ fderivWithOrderLM_eq_of_scalars

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:

• feat: endow test functions with the natural LF topology #31806
  By Dependent Issues (🤖). Happy coding!