feat(Probability): add real-valued PMF normalization and bind lemmas - #1062
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Defines statistical distance as `(1/2) * ∑' a, |p a - q a|` instead of a finite sum. Absolute summability follows from unit mass, so the `MetricSpace (PMF α)` instance and the `StatisticallyClose` API now apply to PMFs on any type, such as `List Bool`. On finite types, `dist_eq` still gives the finite-sum formula; the general formula is `dist_eq_tsum`. This removes `[Fintype α]` from the metric instance, `dist_le_one`, `dist_eq_one_of_disjoint_support`, `dist_bind_le`, `dist_map_le`, and the `StatisticallyClose` lemmas, and `[Fintype Commitment]` from `StatisticallyHiding` and its theorems. Callers that pass these instances explicitly need to drop them, and `dist_eq` no longer holds by `rfl`. The private `sum_toReal` and `bind_apply_toReal` copies in this file are replaced by the public lemmas from #1062. The perfect hiding/binding impossibility for commitments is now a corollary of the statistical version, and the test instantiates it with commitments in `ℕ`.
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Adds general lemmas to `Cslib.Probability.PMF` for working with real-valued masses. The masses of any PMF are summable and sum to one (`tsum_toReal`, `sum_toReal`), the mass of an outcome of `PMF.bind` is the weighted average of the conditional masses (`bind_apply_toReal_tsum`, `bind_apply_toReal`), and expectations of real-valued scores transform as expected under `map`, `bind`, and affine maps. For events, it adds the bounds `toOuterMeasure_le_one` and `toOuterMeasure_ne_top`, complements, positivity, the real-valued form of conditioning with `PMF.filter`, and the law of total probability for `PMF.bind`. These are the PMF facts used by the statistical distance and security-game PRs that follow. Like the rest of the module, they are domain-independent and candidates for Mathlib.
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Adds the five real-valued PMF lemmas needed by the statistical-distance and security-game developments: masses are summable and sum to one, and bind probabilities are weighted sums of conditional probabilities. Normalization and bind formulas cover arbitrary discrete types, with finite-sum corollaries.
These domain-independent lemmas remain in the existing temporary PMF module pending upstreaming to Mathlib. Event, conditioning, and expectation extensions are deferred to their consumers.
Originally composed with Claude Code; revised with Codex to minimize the prerequisite API.