Theorems · Theorem · order theory
IsGLB.biUnion_Ici_eq_Ioi
∀ {α : Type v} [inst : LinearOrder α] {s : Set α} {a : α}, IsGLB s a → a ∉ s → ⋃ x ∈ s, Set.Ici x = Set.Ioi a- Defined in
- Mathlib.Order.Interval.Set.Disjoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.iUnionstatement · cited by 2,483
- LT.lt.leproof · cited by 2,189
- Set.Ioistatement and proof · cited by 1,463
- Set.Icistatement · cited by 1,070
- LE.le.antisymmproof · cited by 507
- lt_of_le_of_neproof · cited by 230
- IsGLBstatement and proof · cited by 213
- Set.mem_iUnion₂proof · cited by 70
- Set.iUnion₂_subsetproof · cited by 48
- Set.Ici_subset_Ioiproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- iUnion_Ici_eq_Ioi_iInfproof · cited by 1
- IsLUB.biUnion_Iic_eq_Iioproof · cited by 1