Research proof index

The same as ModelData but without the propositions. -/ class PreModelData (α : TypeIndex) where TSet : Type u AllPerm : Type u [allPermGroup : Group AllPerm] [allAction : MulAction AllPerm TSet] tSetForget : TSet → StrSet α allPermForget : AllPerm → StrPerm α export PreModelData (TSet AllPerm) attribute [instance] PreModelData.allPermGroup PreModelData....

A preliminary endgame bound. In the $\tau$-minimizer setup, let $k=d[X_1;X_2]$ and let measurable $T_1,T_2,T_3$ satisfy $T_1+T_2+T_3=0$. Put $\delta=I[T_1:T_2]+I[T_2:T_3]+I[T_3:T_1]$ and $c[T_1\#T_2]=d[X_1^0;T_1]-d[X_1^0;X_1]+d[X_2^0;T_2]-d[X_2^0;X_2].$ Then $k\le\delta+\eta c[T_1\#T_2]+\frac{\eta}{2}\bigl(I[T_1:T_3]+I[T_2:T_3]\bigr).$

For a fixed spatial grid cube $I$, every frequency parameter lying in one of the prescribed balls centered at the finite net $\mathcal Z(I)$ also lies in at least one of the frequency regions $\Omega_1(I,f)$. Equivalently, the union of those net balls is contained in the union of the first-stage tile frequency regions.

Maddy's Lemma : Density implies continuity.

Loop.ofPath is continuous, general version.

The indicator of a half-open interval Ioc a b with constant value c is left-continuous: when approached from the left it is eventually constant, so it is continuous within Iio t at t for every t.