feat(Analysis/Convex/Between): add lemmas on affine independence under strict betweenness

[zcyemi]

---

Add lemmas showing that affine independence is preserved when replacing a vertex by a point strictly between two others, and related results for triangles.

deps:

• [ ] depends on: #31498
• [ ] depends on: #31499

[github-actions[bot]]

PR summary d6b7d98695

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ AffineIndependent.comm_left + AffineIndependent.comm_right + AffineIndependent.reverse_of_three + affineIndependent_iff_affineIndependent_of_sbtw + affineIndependent_of_affineIndependent_collinear_ne + affineIndependent_of_sbtw_affineIndependent + affineIndependent_of_sbtw_affineIndependent_inv + affineIndependent_of_sbtw_sbtw + ne_of_affineIndependent_sbtw_sbtw

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).

[zcyemi]

t-convex-geometry

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#31498~~
• ~~leanprover-community/mathlib4#31499~~ By Dependent Issues (🤖). Happy coding!

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.