Proof of `Projecting split paths and preserving endpoint loads` (2nd 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
Induct over the split path. An input port has only its paired output port as a positive-capacity successor. The next input port cannot be the one just visited, because the path is simple; the connecting arc therefore represents an original graph edge. Apply induction to the remaining pairs and preserve both original endpoints and simplicity.
Attribution
Bonnet–Chang, flow projection in Lemma 7.