Proof of `Preprocessing an interval scheduling instance down to a bounded number of live jobs` (2nd statement)
groundedproofs/Lax470956Proofs/Preprocessing.lean · lax-470956
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
One inequality is immediate, since a schedule using only kept jobs is a schedule. The other is the exchange argument: any feasible schedule can be rewritten, one discarded job at a time, into one of no smaller weight that uses only kept jobs.