Chapter 14: partial formalization of Cauchy's arm lemma and rigidity statements

[AItoBit]

Replaces the Chapter 14 skeleton with a partial development of Cauchy's arm lemma and rigidity statements. Includes 15 proofs covering planar and spherical triangles, strict comparison and equality criteria, and the final metric calculation in the polygon induction.

Adds geometric definitions of strictly convex polygons and labeled convex polyhedra. The full planar and spherical arm lemmas and Cauchy's rigidity and dihedral conclusions remain explicit proposition definitions, not proved theorems. The general induction and rigidity proof are still unfinished.

Validation: lake --wfail build FormalBook.Chapter_14 passes on the pinned Lean 4.35.0-rc3 and Mathlib revision. All 15 theorem axiom audits contain only propext, Classical.choice, and Quot.sound. lake env leanchecker --verbose FormalBook.Chapter_14 accepts the compiled module. The Batteries linter passes via lake exe batteries/runLinter FormalBook.Chapter_14. The file also passes the 100-character line-length and whitespace checks.

AI assistance: Codex prepared the supplied Lean development for this repository and checked it.