Theorems · Theorem · order theory
Set.Ioc_union_left
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, a ≤ b → Set.Ioc a b ∪ {a} = Set.Icc a b- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- PartialOrderstatement and proof · cited by 6,410
- Set.Iccstatement and proof · cited by 1,702
- Set.Iocstatement · cited by 971
- Set.singleton_subset_iffproof · cited by 206
- Set.left_mem_Iccproof · cited by 67
- Set.sdiff_union_selfproof · cited by 30
- Set.union_eq_self_of_subset_rightproof · cited by 25
- Set.Icc_sdiff_leftproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Set.Ioc_insert_leftproof · cited by 6
- integrableOn_Icc_iff_integrableOn_Ioc'proof · cited by 2
- Finset.Ioc_insert_leftproof · cited by 1