Proof of `Coupled route sampling with shared vertex images` (4th 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
First sum out all other edge routes. Restrict the uniform vertex assignment to the two distinct edge endpoints, then use the conditional mixture identity.