Research proof index

Strict decrease condition on consecutive μA-slopes for HNFil. This is the analogue of “HN slopes are strictly decreasing”, phrased as the non-comparability statement ¬ μA(i,i+1) ≤ μA(i+1,i+2). The proof is an application of the internal obstruction lemma prop3d7₂.

JHFil_refine_lt_step_payoff proves the stability step condition for the chain JHFil. For each k with JHFil ... k > ⊥ and any strict intermediate z between JHFil ... (k+1) and JHFil ... k, the payoff strictly decreases when refining the step through z.

JHFil_step_payoff_eq_tot proves the first step condition for the chain JHFil. For each index k with JHFil ... k > ⊥, the payoff of the step (JHFil ... (k+1), JHFil ... k) is equal to the total payoff μ (⊥, ⊤).

An isomorphism rewriting a quotient by ker_of_quot_comp_localization. This lemma constructs a LinearEquiv identifying I.val.2 / ker_of_quot_comp_localization I with a quotient of I.val.2 / I.val.1 by the kernel of the localization map CP.f1 I. It is a technical step toward computing the associated primes of the intermediate quotient used in the...

Paper Lemma 2.4 (part 2) localized to an interval I. Assuming convexity of μ on I, this gives a bound between two μmax values obtained from a non-comparable pair x,w. API note: the conclusion is stated as an inequality between μmax on two strict pairs in ℒ.

Paper Lemma 2.4 (part 3) localized to an interval I. This combines lem2d4₁ and lem2d4₂I to compare μA values on two different intervals determined by the non-comparable pair x,w.