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Theorems · Theorem · logic and foundations

Ordinal.bddAbove_of_small

∀ {s : Set Ordinal.{u}} [Small.{u, u + 1} ↑s], BddAbove s
Defined in
Mathlib.SetTheory.Ordinal.Family
Cited by
19 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Small

Around this declaration

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

Ordinal.le_iSup · cited by 19Ordinal.le_iSupOrdinal.iSup_le_iff · cited by 9Ordinal.iSup_le_iffOrdinal.isNormal_derivFamily · cited by 5Ordinal.isNormal_derivFam…Ordinal.nfpFamily_fp · cited by 4Ordinal.nfpFamily_fpOrdinal.lt_iSup_iff · cited by 4Ordinal.lt_iSup_iffOrdinal.lift_cof_iSup_add_one · cited by 4Ordinal.lift_cof_iSup_add…Ordinal.derivFamily_fp · cited by 3Ordinal.derivFamily_fpOrdinal.apply_omega0_of_isNormal · cited by 2Ordinal.apply_omega0_of_i…Ordinal.bddAbove_iff_small · cited by 2Ordinal.bddAbove_iff_smallOrdinal.lsub_le_of_range_subset · cited by 1Ordinal.lsub_le_of_range_…Ordinal.IsNormal.bsup · cited by 1IsNormal.bsupOrdinal.add_iSup · cited by 1Ordinal.add_iSupCategoryTheory.ObjectProperty.strictLimitsClosureStep_strictLimitsClosureIter_eq_self · cited by 1ObjectProperty.strictLimi…Ordinal.iSup_sum · cited by 1Ordinal.iSup_sumOrdinal.mem_closure_tfae · cited by 1Ordinal.mem_closure_tfaeSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemSet.image · cited by 5609Set.imageCardinal · cited by 2598CardinalOrdinal · cited by 1688Ordinalle_of_lt · cited by 1175le_of_ltOrder.succ · cited by 633Order.succBddAbove · cited by 620BddAboveSet.mem_image_of_mem · cited by 371Set.mem_image_of_memSmall · cited by 369SmallCardinal.ord · cited by 266Cardinal.ordupperBounds · cited by 263upperBoundsOrdinal.card · cited by 122Ordinal.cardCardinal.bddAbove_of_small · cited by 37Cardinal.bddAbove_of_smallOrdinal.bddAbove_of_smallCITED BYCITES

Cites14

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

Cited by19

Results whose statement or proof uses this declaration.