Mathlib Map

Theorems · Theorem · logic and foundations

Cardinal.card_ord

∀ (c : Cardinal.{u_1}), c.ord.card = c
Defined in
Mathlib.SetTheory.Ordinal.Basic
Cited by
23 results in Mathlib
Foundations
Depth 78 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.lift_ord · cited by 8Cardinal.lift_ordCardinal.isRegular_succ · cited by 6Cardinal.isRegular_succOrder.cof_eq_cardinalMk · cited by 6Order.cof_eq_cardinalMkOrdinal.cof_ord_le · cited by 5Ordinal.cof_ord_leOrdinal.isNormal_preOmega · cited by 3Ordinal.isNormal_preOmegaCardinal.add_one_of_aleph0_le · cited by 3Cardinal.add_one_of_aleph…Ordinal.isInitial_ord · cited by 3Ordinal.isInitial_ordCardinal.mk_Iio_toType_ord_lt · cited by 2Cardinal.mk_Iio_toType_or…Cardinal.mk_ord_toType · cited by 2Cardinal.mk_ord_toTypeCardinal.lt_power_cof_ord · cited by 2Cardinal.lt_power_cof_ordOrdinal.isInitialIso · cited by 2Ordinal.isInitialIsoCardinal.card_le_of_le_ord · cited by 1Cardinal.card_le_of_le_ordCategoryTheory.SmallCategoryCardinalLT.exists_equivalence · cited by 1SmallCategoryCardinalLT.e…CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_ordinal · cited by 1generatingMonomorphisms.e…Cardinal.lt_univ · cited by 1Cardinal.lt_univCardinal · cited by 2598CardinalCardinal.mk · cited by 942Cardinal.mkCardinal.ord · cited by 266Cardinal.ordOrdinal.type · cited by 207Ordinal.typeIsWellOrder · cited by 171IsWellOrderOrdinal.card · cited by 122Ordinal.cardCardinal.inductionOn · cited by 19Cardinal.inductionOnCardinal.exists_ord_eq · cited by 8Cardinal.exists_ord_eqOrdinal.card_type · cited by 7Ordinal.card_typeCardinal.card_ordCITED BYCITES

Cites9

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

Cited by24

Results whose statement or proof uses this declaration.