refactor(Analysis): golf Mathlib/Analysis/SpecialFunctions/Gaussian/FourierTransform

[yuanyi-350]

• shortens the verticalIntegral_norm_le proof by replacing the case split on c with Set.abs_sub_left_of_mem_uIcc

Extracted from #37968

[github-actions]

PR summary 38c35d74ba

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

No declarations were harmed in the making of this PR! 🐙

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.

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No changes to strong technical debt.

No changes to weak technical debt.

[yuanyi-350]

I ran a profiler comparison for the changed declarations in this PR.

Results (seconds, Elab.definition.value from trace.profiler):

• GaussianFourier.verticalIntegral_norm_le: 1.067870 -> 1.039139 (-2.69%)

Overall:

• GaussianFourier.verticalIntegral_norm_le is modestly faster after this refactor.
• No regressions showed up among the changed declarations.