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Theorems · Theorem · logic and foundations

Ordinal.lsub_le_iff

Deprecated since 2026-03-27Mathlib marks this declaration as deprecated.

∀ {ι : Type u_3} {f : ι → Ordinal.{max u_4 u_3}} {a : Ordinal.{max u_3 u_4}}, Ordinal.lsub f ≤ a ↔ ∀ (i : ι), f i < a
Defined in
Mathlib.SetTheory.Ordinal.Family
Cited by
6 results in Mathlib
Foundations
Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Ordinal.lsub_le · cited by 6Ordinal.lsub_leOrdinal.iSup_eq_lsub_iff · cited by 1Ordinal.iSup_eq_lsub_iffOrdinal.lsub_empty · cited by 1Ordinal.lsub_emptyOrdinal.exists_fundamental_sequence · cited by 0Ordinal.exists_fundamenta…Ordinal.lt_lsub_iff · cited by 0Ordinal.lt_lsub_iffOrdinal.blsub_type · cited by 0Ordinal.blsub_typeOrdinal · cited by 1688OrdinalOrdinal.lsub · cited by 43Ordinal.lsubOrdinal.iSup_add_one_le_iff · cited by 1Ordinal.iSup_add_one_le_i…Ordinal.lsub_le_iffCITED BYCITES

Cites3

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Cited by6

Results whose statement or proof uses this declaration.