Proof of `Graph-route distributions from high-value split flows` (2nd statement)
groundedproofs/Lax263307Proofs/RouteDistributions.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 registered arc-to-path theorem. Enumerate the finite path-flow support, retain the minus-to-plus commodities, and choose their projected graph routes. Each retained commodity has routed mass at least 1/gamma. The capacity-arc count bounds the weighted membership feature by the original split flow's arc load, which is at most the vertex capacity.