feat: add euclid book i constructions (i.1, i.2, i.3, i.7, i.9)

[slamdunktiger]

Summary

Five propositions from Euclid's Elements, Book I, novel to mathlib4:

Prop	Content
I.1	Equilateral triangle construction
I.2	Copy segment to a point
I.3	Cut shorter segment from longer
I.7	Uniqueness/perpendicularity (equidistant points)
I.9	Angle bisection existence

All theorems formalized in Lean 4 using EuclideanSpace ℝ (Fin 2) with dist, inner, Wbtw. All proofs ZERO sorry, verified with lake build.

Author: Warren Wong

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Recreated as a fresh PR after #42464 was locked (head branch history diverged, GitHub refused reopen).

[github-actions]

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[github-actions]

PR summary 21c5b6fab5

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)

+ angle
+ angle_bisector_exists
+ cut_segment
+ equidistant_implies_perp
+ equilateral_triangle_exists
+ segment_copy
+ thirdVertex
- mathlibLeanOptions
- mathlibOnlyLinters
- mathlibTestOptions

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 -- pending)

Computed after the build finishes.

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 21c5b6fab5
Reference commit b2418b0404

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).

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⚠️ Workflow documentation reminder

This PR modifies files under .github/workflows/.
Please update docs/workflows.md if the workflow inventory, triggers, or behavior changed.

Modified workflow files:

• .github/workflows/lean_action_ci.yml

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note: file lakefile.lean was removed.
Please create a follow-up pull request adding a module deprecation. Thanks!

[grunweg]

Hello from triage! Can you comment on whether you used AI for this project? Thanks! (Per mathlib's AI policy, this is not forbidden in principle, but its usage must be disclosed.)
I have labelled it as LLM-generated since it looks so - but can you please confirm whether this is correct and (if so), how you've used AI?

[eric-wieser]

Mathlib cannot depend on itself, especially since this PR also deletes the mathlib lakefile!