Theorems · Theorem · logic and foundations
Cardinal.mk_Iio_real
∀ (a : ℝ), Cardinal.mk ↑(Set.Iio a) = Cardinal.continuum
The cardinality of the interval $(-∞, a)$.
- Defined in
- Mathlib.Analysis.Real.Cardinality
- Cited by
- 1 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Set.Elemstatement · cited by 7,166
- Set.imageproof · cited by 5,609
- Cardinalstatement · cited by 2,598
- le_antisymmproof · cited by 2,068
- Set.Ioiproof · cited by 1,463
- Set.Iiostatement and proof · cited by 1,166
- Cardinal.mkstatement · cited by 942
- add_sub_cancel_rightproof · cited by 187
- Cardinal.continuumstatement · cited by 60
- Cardinal.mk_set_leproof · cited by 14
- Cardinal.mk_realproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Cardinal.mk_Iic_realproof · cited by 0