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Theorems · Definition · logic and foundations

Ordinal.card

Ordinal.{u_1} → Cardinal.{u_1}

The cardinal of an ordinal is the cardinality of any type on which a relation with that order type is defined.

Defined in
Mathlib.SetTheory.Ordinal.Basic
Cited by
122 results in Mathlib
Foundations
Depth 28 from the axioms, rests on 105 definitions · uses propext, Quot.sound
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Around this declaration

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

Ordinal.IsInitial · cited by 28Ordinal.IsInitialCardinal.card_ord · cited by 23Cardinal.card_ordOrdinal.bddAbove_of_small · cited by 19Ordinal.bddAbove_of_smallCardinal.lt_ord · cited by 13Cardinal.lt_ordCardinal.mk_toType · cited by 12Cardinal.mk_toTypeCardinal.isSuccLimit_ord · cited by 11Cardinal.isSuccLimit_ordOrdinal.card_le_card · cited by 10Ordinal.card_le_cardCardinal.ord_le · cited by 10Cardinal.ord_leCardinal.ord_aleph0 · cited by 9Cardinal.ord_aleph0Cardinal.ord_univ · cited by 8Cardinal.ord_univCardinal.mk_Iio_ordinal · cited by 8Cardinal.mk_Iio_ordinalOrdinal.lift_card · cited by 7Ordinal.lift_cardOrdinal.card_type · cited by 7Ordinal.card_typeCardinal.gc_ord_card · cited by 6Cardinal.gc_ord_cardOrdinal.card_add · cited by 6Ordinal.card_addCardinal · cited by 2598CardinalOrdinal · cited by 1688OrdinalQuotient.map · cited by 7Quotient.mapWellOrder.α · cited by 5WellOrder.αOrdinal.cardCITED BYCITES

Cites4

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

Cited by125

Results whose statement or proof uses this declaration.