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Theorems · Theorem · order theory

Set.Ioi_subset_Ici_self

∀ {α : Type u_1} [inst : Preorder α] {a : α}, Set.Ioi a ⊆ Set.Ici a
Defined in
Mathlib.Order.Interval.Set.Basic
Cited by
34 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Filter.atTop_basis_Ioi · cited by 10Filter.atTop_basis_IoiIci_mem_nhds · cited by 9Ici_mem_nhdsborel_eq_generateFrom_Iio · cited by 6borel_eq_generateFrom_Iioclosure_Ioi' · cited by 5closure_Ioi'Fin.image_addNat_Ioi · cited by 5Fin.image_addNat_IoiSet.Ioi_subset_Ici · cited by 5Set.Ioi_subset_IciSet.OrdConnected.mem_nhdsGT · cited by 4OrdConnected.mem_nhdsGTFin.image_natAdd_Ioi · cited by 4Fin.image_natAdd_IoiIci_mem_nhdsSet_Icc · cited by 3Ici_mem_nhdsSet_IcccontentRegular_rieszContent · cited by 3contentRegular_rieszConte…MeasureTheory.integral_deriv_smul_comp_Ioi · cited by 2MeasureTheory.integral_de…Set.mem_Ici_of_Ioi · cited by 2Set.mem_Ici_of_IoiMeasureTheory.tendsto_limUnder_of_hasDerivAt_of_integrableOn_Ioi · cited by 2MeasureTheory.tendsto_lim…convexOn_zpow · cited by 2convexOn_zpowStieltjesFunction.outer_Ioc · cited by 2StieltjesFunction.outer_I…Set · cited by 53352SetPreorder · cited by 7952PreorderSet.Ioi · cited by 1463Set.Ioile_of_lt · cited by 1175le_of_ltSet.Ici · cited by 1070Set.IciSet.Ioi_subset_Ici_selfCITED BYCITES

Cites5

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

  • Setstatement · cited by 53,352
  • Preorderstatement and proof · cited by 7,952
  • Set.Ioistatement and proof · cited by 1,463
  • le_of_ltproof · cited by 1,175
  • Set.Icistatement · cited by 1,070

Cited by34

Results whose statement or proof uses this declaration.