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Theorems · Theorem · logic and foundations

Ordinal.lt_iSup_iff

∀ {ι : Type u_3} {f : ι → Ordinal.{u}} {a : Ordinal.{u}} [Small.{u, u_3} ι], a < ⨆ i, f i ↔ ∃ i, a < f i

lt_ciSup_iff' whenever the input type is small in the output universe.

Defined in
Mathlib.SetTheory.Ordinal.Family
Cited by
4 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Small
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Ordinal.lt_nfpFamily_iff · cited by 2Ordinal.lt_nfpFamily_iffOrdinal.lt_nfp_iff · cited by 2Ordinal.lt_nfp_iffnot_surjective_of_ordinal · cited by 1not_surjective_of_ordinalAcc.mem_range_rank_of_le · cited by 1Acc.mem_range_rank_of_leiSup · cited by 2415iSupOrdinal · cited by 1688OrdinalSmall · cited by 369SmallOrdinal.bddAbove_of_small · cited by 19Ordinal.bddAbove_of_smalllt_ciSup_iff' · cited by 4lt_ciSup_iff'Ordinal.lt_iSup_iffCITED BYCITES

Cites5

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Cited by4

Results whose statement or proof uses this declaration.