Proof of `Projecting split paths and preserving endpoint loads` (1st statement)
groundedproofs/Lax263307Proofs/SplitPathProjection.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
The expanded list contains one forward capacity arc per occurrence of the original vertex. Cross arcs join output ports to input ports and cannot be capacity arcs. On a simple route, a vertex occurs either once or not at all.
Attribution
Bonnet–Chang, endpoint-inclusive load accounting in Lemma 7.