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Theorems · Definition · logic and foundations

Ordinal.univ

Ordinal.{max (u + 1) v}

The ordinal univ.{u, v} is the order type of Ordinal.{u} or Cardinal.{u}, as an element of Ordinal.{v} (when u < v).

Defined in
Mathlib.SetTheory.Ordinal.Univ
Cited by
18 results in Mathlib
Foundations
Depth 40 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.

Cardinal.ord_univ · cited by 8Cardinal.ord_univOrdinal.liftPrincipalSeg · cited by 6Ordinal.liftPrincipalSegOrdinal.type_lt_cardinal · cited by 2Ordinal.type_lt_cardinalOrdinal.type_lt_ordinal · cited by 2Ordinal.type_lt_ordinalOrdinal.cof_univ · cited by 1Ordinal.cof_univCardinal.preAleph_univ · cited by 1Cardinal.preAleph_univCardinal.aleph_univ · cited by 0Cardinal.aleph_univOrdinal.univ_id · cited by 0Ordinal.univ_idOrdinal.univ_umax · cited by 0Ordinal.univ_umaxCardinal.preAleph_symm_univ · cited by 0Cardinal.preAleph_symm_un…Ordinal.omega_univ · cited by 0Ordinal.omega_univOrdinal.lift_univ · cited by 0Ordinal.lift_univOrdinal.card_univ · cited by 0Ordinal.card_univOrdinal.preOmega_univ · cited by 0Ordinal.preOmega_univCardinal.beth_univ · cited by 0Cardinal.beth_univOrdinal · cited by 1688OrdinalOrdinal.type · cited by 207Ordinal.typeOrdinal.lift · cited by 86Ordinal.liftOrdinal.univCITED BYCITES

Cites3

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.