Theorems · Theorem · order theory
Set.Ico_inter_Ico
∀ {α : Type u_1} [inst : LinearOrder α] {a₁ a₂ b₁ b₂ : α},
Set.Ico a₁ b₁ ∩ Set.Ico a₂ b₂ = Set.Ico (max a₁ a₂) (min b₁ b₂)- Defined in
- Mathlib.Order.Interval.Set.LinearOrder
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 18 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.
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.Icostatement · cited by 799
Cited by4
Results whose statement or proof uses this declaration.
- isPiSystem_Icoproof · cited by 2
- Set.Ico_disjoint_Icoproof · cited by 2
- Finset.Ico_inter_Icoproof · cited by 1
- isPiSystem_Ico_memproof · cited by 0