Research proof index

Rewrites the probability over the large r space as a sequential probability, sampling r_last first, then r_init.

Generic Probability Splitting Lemma (via Equivalence) This lemma proves that a single probability statement over a uniform distribution on a type α can be rewritten as a sequential probability statement over two smaller, independent distributions γ and δ, given an equivalence e : α ≃ γ × δ. This is a formal "change of variables" for probabilit...

Unrolls Pr_{ let x ← D; let y ← D }[P x y] into a sum of the form ∑' (x × y), (if P x y then 1 else 0).

Unrolls Pr_{ let x ← D }[P x] into a sum of the form ∑' x, Pr[x] * (if P x then 1 else 0).

Version of boolBiasAdvantage_eq_boolDistAdvantage_uniformBool_branch with a shared sampled prefix before the real/random branch is chosen.

Four-way disagreement+bad additive bind bound. A merge of probEvent_bind_le_add_of_disagree with the three-world probEvent_bind_le_add_bad_of_disagree: the disagreement set D (a table-level exceptional set, not a bad event) is charged its full mass ε₁; everywhere off D the my-world is bounded by the oc-world plus the per-shared-sample...