Mathlib Map

Theorems · Theorem · order theory

Set.Ico_union_Ico

∀ {α : Type u_1} [inst : LinearOrder α] {a b c d : α},
  min a b ≤ max c d → min c d ≤ max a b → Set.Ico a b ∪ Set.Ico c d = Set.Ico (min a c) (max b d)
Defined in
Mathlib.Order.Interval.Set.LinearOrder
Cited by
2 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Finset.Ico_union_Ico · cited by 2Finset.Ico_union_IcoSet.Ico_union_Ico' · cited by 1Set.Ico_union_Ico'Set · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.Ico · cited by 799Set.IcoSet.Ico_union_IcoCITED BYCITES

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 by2

Results whose statement or proof uses this declaration.