Proof of `Conditioning preserves bounded costs and total mass`
groundedproofs/Lax263307Proofs/ConditionedCosts.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
Conditioning preserves the unit-interval bounds and total mass, fixes the chosen vertices to one, and preserves positivity at every positive-cost step.
Proof strategy
Divide the monotonicity inequalities and mass equation by the positive conditioning moment. Inserting a vertex already in the conditioning set does not change the set.
Attribution
Bonnet–Chang, Section 4.1.