Subgradient-lean: Formal Proofs of Subgradient Method Convergence in Lean 4

`subgradient-lean` is a Lean 4 / Mathlib library formalising the classical convergence theorem for the subgradient method on convex, possibly non-smooth objectives. The library defines the subgradient predicate `IsSubgradientAt`, packages a full trajectory in `SubgradientRun`, proves the exact squared-distance identity for a subgradient step, derives the per-step distance bound, telescopes the resulting inequalities, and proves the `O(1/sqrt K)` running-minimum guarantee. The development contains zero `sorry`, zero `admit`, and uses standard Lean/Mathlib axioms only. It provides a checked baseline theorem for non-smooth convex optimisation and a reusable component for formal work on learning theory and AI safety.