Proof of `A good coupled sample with bounded total route size` (1st statement)
groundedproofs/Lax263307Proofs/CoupledSamplingBounds.lean · lax-263307
What this proof establishes
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Apply the union bound over ordered source-edge pairs. Every nonincident pair has the independent route law; its interaction probability is at most collision plus adjacency probability. There are at most m² pairs.