Theorems · Theorem · logic and foundations
Cardinal.mk_Ioi_real
∀ (a : ℝ), Cardinal.mk ↑(Set.Ioi a) = Cardinal.continuum
The cardinality of the interval $(a, ∞)$.
- Defined in
- Mathlib.Analysis.Real.Cardinality
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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
- Set.univproof · cited by 3,945
- Cardinalstatement and proof · cited by 2,598
- LT.lt.leproof · cited by 2,189
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- Set.Ioistatement and proof · cited by 1,463
- Set.Iioproof · cited by 1,166
- Set.Iicproof · cited by 1,111
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.mk_Ioo_realproof · cited by 5
- Cardinal.mk_Iio_realproof · cited by 1
- Cardinal.mk_Ici_realproof · cited by 0