Proof of `Collision and length bounds for independently sampled paths` (2nd statement)
groundedproofs/Lax263307Proofs/PathSampling.lean · lax-263307
What this proof establishes
no assumptions
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
If two outcomes intersect, at least one vertex witnesses that event. Sum the resulting indicator bound against the product outcome probabilities, interchange the sums, and factor each vertex contribution into the product of its two identical loads.