Proof of `Coupled route sampling with shared vertex images` (3rd statement)
groundedproofs/Lax263307Proofs/CoupledRouteSampling.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
Sum out all other edge routes. Restrict the uniform vertex assignment to the four distinct endpoints, then apply the independent endpoint mixture identity.