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Theorems · Theorem · logic and foundations

Cardinal.ord_cardinalMk

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : WellFoundedLT α] [IsRegularCardinalOrder α],
  (Cardinal.mk α).ord = Ordinal.type fun x1 x2 => x1 < x2
Defined in
Mathlib.SetTheory.Cardinal.Cofinality.Enum
Cited by
1 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderWellFoundedLTIsRegularCardinalOrder
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Around this declaration

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

Order.type_eq_of_isCofinal · cited by 0Order.type_eq_of_isCofinalLinearOrder · cited by 8572LinearOrderCardinal · cited by 2598CardinalOrdinal · cited by 1688OrdinalCardinal.mk · cited by 942Cardinal.mkWellFoundedLT · cited by 491WellFoundedLTCardinal.ord · cited by 266Cardinal.ordOrdinal.type · cited by 207Ordinal.typeIsWellOrder · cited by 171IsWellOrderIsRegularCardinalOrder · cited by 17IsRegularCardinalOrderOrder.cof_eq_cardinalMk · cited by 6Order.cof_eq_cardinalMkOrder.ord_cof_eq_type_lt · cited by 2Order.ord_cof_eq_type_ltCardinal.ord_cardinalMkCITED BYCITES

Cites11

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Cited by1

Results whose statement or proof uses this declaration.