Theorems · Theorem · logic and foundations
Cardinal.mk_Ioo_real
∀ {a b : ℝ}, a < b → Cardinal.mk ↑(Set.Ioo a b) = Cardinal.continuumThe cardinality of the interval $(a, b)$.
- Defined in
- Mathlib.Analysis.Real.Cardinality
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.Elemstatement and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- Cardinalstatement and proof · cited by 2,598
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- Set.Ioostatement and proof · cited by 1,214
- sub_selfproof · cited by 996
- le_transproof · cited by 985
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.continuumstatement and proof · cited by 60
Cited by5
Results whose statement or proof uses this declaration.
- Cardinal.mk_Icc_realproof · cited by 2
- Cardinal.mk_Ioc_realproof · cited by 1
- Cardinal.mk_Ico_realproof · cited by 1
- Cardinal.Real.Ioo_countable_iffproof · cited by 0