Theorems · Theorem · order theory
Nat.card_Ioo
∀ (a b : ℕ), (Finset.Ioo a b).card = b - a - 1
- Defined in
- Mathlib.Order.Interval.Finset.Nat
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.cardstatement · cited by 2,327
- Finset.Ioostatement · cited by 185
Cited by7
Results whose statement or proof uses this declaration.
- schnirelmannDensity_le_of_notMemproof · cited by 2
- Fin.card_Ioiproof · cited by 1
- PNat.card_Iooproof · cited by 1
- Nat.grahamConjecture_of_squarefreeproof · cited by 0
- Fin.card_Iooproof · cited by 0
- add_eq_univ_of_one_le_schirelmannDensity_add_schnirelmannDensityproof · cited by 0
- Set.ncard_Ioo_natproof · cited by 0