Lax Lean Archive

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Proof of `The dynamic program for interval scheduling, and its state space` (2nd statement)

groundedproofs/Lax470956Proofs/DynamicProgram.lean · lax-470956

What this proof establishes

no assumptions

def✓Lax470956.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.

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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.