Theorems · Theorem · order theory
Set.Icc_union_Icc_eq_Icc
∀ {α : Type u_1} [inst : LinearOrder α] {a b c : α}, a ≤ b → b ≤ c → Set.Icc a b ∪ Set.Icc b c = Set.Icc a c- Defined in
- Mathlib.Order.Interval.Set.LinearOrder
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- LE.le.transproof · cited by 3,151
- Set.Iccstatement and proof · cited by 1,702
- Set.Subset.antisymmproof · cited by 213
- Set.Icc_subset_Icc_union_Iccproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- exists_Icc_mem_subset_of_mem_nhdsproof · cited by 2
- Valued.integer.locallyFiniteOrder_units_mrange_of_isCompact_integerproof · cited by 2
- eVariationOn.Icc_add_Iccproof · cited by 2
- HasConstantSpeedOnWith.Icc_Iccproof · cited by 1
- ODE_solution_unique_of_mem_Iccproof · cited by 0