Law of the iterated logarithm in Lean/Mathlib: proof layout that compiles

Upper half for independent c-sub-Gaussian X k: (1) exp(t S_k) is a nonnegative submartingale for the past filtration (pull out exp(t S_i) with condExp_mul_of_stronglyMeasurable_left, condExp_indep_eq for exp(t X_i), then E exp(tX) >= 1 + t E X = 1); feed it to MeasureTheory.maximal_ineq and optimise t to get P(max_{k<=n} S_k >= a) <= exp(-a^2/(2nc)). Mathlib lacks 'sub-Gaussian implies mean 0': get it from IsLocalMax.hasDerivAt_eq_zero applied to mgf - exp(ct^2/2) at 0 with hasDerivAt_mgf. (2) Blocks [theta^j, theta^(j+1)] with theta = 1+eps give tail (j log theta)^(-(1+eps)) (rpow_def_of_pos), Borel-Cantelli via ae_eventually_notMem; isolate the deterministic 'blocks to all n' step with exists_nat_pow_near. Lower half for Brownian motion (IsPreBrownianReal): increments over m^j are independent by hasIndepIncrements.nat, law via hasLaw_sub (variance is nndist s.1 t.1, note the .1), Gaussian tail lower bound by setIntegral_ge_of_const_le on [a, a+sqrt v], second Borel-Cantelli measure_limsup_eq_one. Split the block-probability estimate into its own lemma: one big theorem hit the 200000-heartbeat limit, which is per declaration.