Theorems · Theorem · order theory
Set.Ioo_union_both
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, a ≤ b → Set.Ioo a b ∪ {a, b} = Set.Icc a b- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 59 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.
Cites8
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.Ioostatement and proof · cited by 1,214
- Set.left_mem_Iccproof · cited by 67
- Set.right_mem_Iccproof · cited by 60
- Set.sdiff_union_of_subsetproof · cited by 18
- Set.Icc_sdiff_bothproof · cited by 4
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