Mathlib Map

Theorems · Theorem · general topology

Filter.Ici_mem_atTop

∀ {α : Type u_3} [inst : Preorder α] (a : α), Set.Ici a ∈ Filter.atTop
Defined in
Mathlib.Order.Filter.AtTopBot.Defs
Cited by
37 results in Mathlib
Foundations
Depth 53 from the axioms · uses propext, Quot.sound
Assumes
Preorder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Monotone.tendstoLocallyUniformly_of_forall_tendsto · cited by 4Monotone.tendstoLocallyUn…MeasureTheory.LocallyIntegrableOn.integrableOn_of_isBigO_atTop · cited by 4LocallyIntegrableOn.integ…isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_le · cited by 2isCompact_setOfPred_finit…MeasureTheory.integral_deriv_smul_comp_Ioi · cited by 2MeasureTheory.integral_de…BoundedVariationOn.vectorMeasure_Ici · cited by 2BoundedVariationOn.vector…AntitoneOn.tsum_comp_add_le_integral · cited by 2AntitoneOn.tsum_comp_add_…HasFPowerSeriesWithinOnBall.tendsto_partialSum_prod · cited by 2HasFPowerSeriesWithinOnBa…intermediate_value_Ici · cited by 2intermediate_value_Iciintermediate_value_Ici' · cited by 2intermediate_value_Ici'Filter.disjoint_atBot_atTop · cited by 2Filter.disjoint_atBot_atT…not_integrableOn_Ici_inv · cited by 2not_integrableOn_Ici_invFilter.disjoint_atTop_atBot · cited by 2Filter.disjoint_atTop_atB…BoundedVariationOn.exists_tendsto_atTop · cited by 2BoundedVariationOn.exists…BoundedVariationOn.tendsto_eVariationOn_Ici_zero · cited by 1BoundedVariationOn.tendst…ProbabilityTheory.tsum_prob_mem_Ioi_lt_top · cited by 1ProbabilityTheory.tsum_pr…Set · cited by 53352SetFilter · cited by 8121FilterPreorder · cited by 7952PreorderFilter.atTop · cited by 2405Filter.atTopSet.Ici · cited by 1070Set.IciFilter.mem_atTop · cited by 9Filter.mem_atTopFilter.Ici_mem_atTopCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by37

Results whose statement or proof uses this declaration.