[Merged by Bors] - feat(Geometry/Euclidean/Sphere): add lemmas about points on a sphere

[Scarlett-le]

Adds three lemmas to Mathlib/Geometry/Euclidean/Sphere/Basic.lean.

• Sphere.ne_center_of_mem_of_mem_of_ne: a point of a sphere that differs
  from another point of the sphere is not its center. Extracted at a
  reviewer's suggestion; this fact was reproved inline four times across
  feat(Geometry/Euclidean/Angle): add the Alternate segment theorem #41121 and feat(Geometry/Euclidean/Angle): the unoriented angle at the center in terms of the angle at the circumference #41123.

• norm_vsub_center_eq_radius: for a point p on a sphere s,
  ‖p -ᵥ s.center‖ = s.radius. This pattern occurs ten times in feat(Geometry/Euclidean/Sphere): define arcs on spheres #34164 and
  four more times in the present file (twice in inner_vsub_center_vsub_pos
  and twice in Sphere.dist_center_lt_radius_of_sbtw); those four in-file
  occurrences are golfed to use it here.

• Sphere.center_mem_affineSpan_pair_iff_isDiameter: for two distinct points
  of a sphere, the center lies on the line through them if and only if those
  points are the endpoints of a diameter.

No mathematical content changes; the existing proofs are only shortened.

[github-actions]

PR summary e50a6ccb22

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ Sphere.ne_center_of_mem_of_mem_of_ne
+ center_mem_affineSpan_pair_iff_isDiameter
+ norm_vsub_center_eq_radius

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 e50a6cc).

• +3 new declarations
• −0 removed declarations

+EuclideanGeometry.Sphere.center_mem_affineSpan_pair_iff_isDiameter
+EuclideanGeometry.Sphere.ne_center_of_mem_of_mem_of_ne
+EuclideanGeometry.norm_vsub_center_eq_radius

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit e50a6ccb22
Reference commit b2b4255167

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).

[jsm28]

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by jsm28.

[j-loreaux]

Thanks!

[mathlib-auto-merge]

As this PR is labelled auto-merge-after-CI, we are now sending it to bors:

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Lint style
• ci (staging) / Post-Build Step
• ci (staging) / Post-CI job
• ci (staging) / Test and lint
• ci (staging) / Build