Theorems · Definition · order theory
Set.Ico
{α : Type u_1} → [Preorder α] → α → α → Set αIco a b is the left-closed right-open interval $[a, b)$.
- Defined in
- Mathlib.Order.Interval.Set.Defs
- Cited by
- 799 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 11 definitions · uses no axioms
- Assumes
- Preorder
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
- Preorderstatement and proof · cited by 7,952
- Set.ofPredproof · cited by 6,101
Cited by809
Results whose statement or proof uses this declaration.
- Finset.coe_Icostatement · cited by 66
- ZSpan.fundamentalDomainproof · cited by 48
- Set.Ico_subset_Icc_selfstatement · cited by 41
- Set.Ioo_subset_Ico_selfstatement · cited by 29
- Set.Ico_eq_emptystatement and proof · cited by 24
- closure_ballproof · cited by 20
- Set.left_mem_Icostatement · cited by 18
- NumberField.mixedEmbedding.fundamentalCone.paramSetproof · cited by 18
- measurableSet_Icostatement · cited by 17
- interior_Icostatement · cited by 12
- Set.mem_Icostatement · cited by 11
- Set.Ico_toDualstatement · cited by 11
Showing the 200 most cited of 809.