perf(LinearAlgebra/RootSystem/GeckConstruction/Semisimple):replace generic search with a more exp proof

[FawadHa1der]

generic search replaced by simplification and case splitting. Improves the local heartbeat/performance of the file. Does not affect the overall build.

Hopefully bench could show some numbers.

[github-actions]

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[FawadHa1der]

!bench

[leanprover-radar]

Benchmark results for ec8668d against 056733e are in. There are significant results. @FawadHa1der

• ✅ build//instructions: -72.9G (-0.05%)

Large changes (1✅)

• ✅ build/module/Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple//instructions: -92.2G (-41.88%)

[github-actions]

PR summary 658d0dd1fc

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

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.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 658d0dd).

• +0 new declarations
• −0 removed declarations

No declaration differences.

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 658d0dd1fc
Reference commit 056733e1c3

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).

[felixpernegger]

Suggested change

	ext i j
	simp [Pi.single_apply]
	split_ifs <;> simp
	ext i j
	simp [Pi.single_apply]
	split_ifs <;> simp

Indendation. Great PR!