Theorems · Definition · order theory
Set.uIoo
{α : Type u_1} → [LinearOrder α] → α → α → Set αuIoo a b is the set of elements lying between a and b, with a and b not included.
Note that we define it more generally in a lattice as Set.Ioo (a ⊓ b) (a ⊔ b). In a product type,
uIoo corresponds to the bounding box of the two elements.
- Cited by
- 68 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.Iooproof · cited by 1,214
Cited by68
Results whose statement or proof uses this declaration.
- Set.uIoo_of_lestatement · cited by 5
- intervalIntegral.integral_congr_uIoostatement and proof · cited by 4
- Set.uIoo_of_ltstatement · cited by 4
- Set.uIoo_of_gestatement · cited by 3
- taylor_mean_remainderstatement and proof · cited by 2
- closure_uIoostatement · cited by 2
- Set.uIoo_of_gtstatement · cited by 2
- Set.uIoo_subset_uIcc_selfstatement · cited by 2
- exists_eq_interval_average_of_nullSingletonClassstatement and proof · cited by 2
- taylor_integral_remainder_auxproof · cited by 2
- taylor_mean_remainder_lagrangestatement and proof · cited by 1
- taylor_mean_remainder_lagrange_iteratedDerivstatement and proof · cited by 1