Theorems · Theorem · order theory
iUnion_Ici_eq_Ioi_iInf
∀ {ι : Sort u} {R : Type u_1} [inst : CompleteLinearOrder R] {f : ι → R},
⨅ i, f i ∉ Set.range f → ⋃ i, Set.Ici (f i) = Set.Ioi (⨅ i, f i)- Defined in
- Mathlib.Order.Interval.Set.Disjoint
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLinearOrder
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
- Set.rangestatement and proof · cited by 4,705
- Set.iUnionstatement and proof · cited by 2,483
- iInfstatement and proof · cited by 1,690
- Set.Ioistatement · cited by 1,463
- Set.Icistatement and proof · cited by 1,070
- Set.iUnion_congr_Propproof · cited by 374
- CompleteLinearOrderstatement and proof · cited by 126
- Set.iUnion_existsproof · cited by 45
- Set.iUnion_iUnion_eq'proof · cited by 21
- isGLB_iInfproof · cited by 7
- IsGLB.biUnion_Ici_eq_Ioiproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- iUnion_Iic_eq_Iio_iSupproof · cited by 0