BoxIntegral.IntegrationParams.hasBasis_toFilterDistortion

theorem BoxIntegral.IntegrationParams.hasBasis_toFilterDistortion : ∀ {ι : Type u_1} [inst : Fintype ι] (l : BoxIntegral.IntegrationParams) (I : BoxIntegral.Box ι) (c : NNReal), (l.toFilterDistortion I c).HasBasis l.RCond fun r => {π | l.MemBaseSet I c r π}

This theorem, `BoxIntegral.IntegrationParams.hasBasis_toFilterDistortion`, states that for any finite-dimensional type `ι`, any integration parameters `l`, any box `I`, and any nonnegative real number `c`, the filter derived from `l`, `I` and `c`, `BoxIntegral.IntegrationParams.toFilterDistortion l I c`, has a basis which is characterized by the predicate `BoxIntegral.IntegrationParams.RCond l`. The elements of this basis are those functions `r` which satisfy the property that all of the tagged partitions `π` belong to the base set `BoxIntegral.IntegrationParams.MemBaseSet l I c r π`. In simpler terms, the theorem defines the conditions under which a function belongs to the basis of a specific filter in the context of Box Integration.

More concisely: For any finite-dimensional type `ι`, integration parameters `l`, box `I`, and nonnegative real number `c`, the filter derived from `l`, `I`, and `c` in Box Integration has a basis consisting of functions `r` that satisfy `BoxIntegral.IntegrationParams.RCond l` and belong to the base set `BoxIntegral.IntegrationParams.MemBaseSet l I c π` for all tagged partitions `π`.