Theorems · Theorem · order theory
Set.uIoc_eq_union
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, Set.uIoc a b = Set.Ioc a b ∪ Set.Ioc b a- Cited by
- 8 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.Iocstatement and proof · cited by 971
- le_totalproof · cited by 294
- sup_of_le_leftproof · cited by 218
- inf_of_le_leftproof · cited by 186
- Set.uIocstatement · cited by 182
- sup_of_le_rightproof · cited by 143
- inf_of_le_rightproof · cited by 128
- Set.union_emptyproof · cited by 78
- Set.empty_unionproof · cited by 52
- Set.Ioc_eq_emptyproof · cited by 38
Cited by8
Results whose statement or proof uses this declaration.
- intervalIntegrable_iffproof · cited by 29
- MeasureTheory.ae_restrict_uIoc_eqproof · cited by 1
- MeasureTheory.ae_uIoc_iffproof · cited by 1
- MeasureTheory.AEStronglyMeasurable.aestronglyMeasurable_uIoc_iffproof · cited by 0
- Set.forall_uIoc_iffproof · cited by 0
- Set.mem_uIocproof · cited by 0
- Set.notMem_uIocproof · cited by 0
- aemeasurable_uIoc_iffproof · cited by 0