Lax Lean Archive

Proof of `The Dynamic Program for Interval Scheduling, and Its State Space` (2nd statement)

groundedproofs/Lax888481Proofs/DynamicProgram.lean · lax-888481

What this proof establishes

no assumptions

def✓Lax888481.DynamicProgram (2nd statement)

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

In the paper

  • page 5 of this submission's paper

Description

Lemma 6, by induction on the time index: the base case is optAtzerooptAt_zero, which realises a state at time zero by the schedule that places exactly its occupants, and the step is optAtsuccoptAt_succ, which matches each predecessor state against the schedules extending it.