Theorems · Theorem · order theory
Set.Iio_union_right
∀ {α : Type u_1} [inst : PartialOrder α] {a : α}, Set.Iio a ∪ {a} = Set.Iic a- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.extproof · cited by 2,266
- Set.Iiostatement · cited by 1,166
- Set.Iicstatement · cited by 1,111
- le_iff_lt_or_eqproof · cited by 26
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.mk_Ioi_realproof · cited by 3
- integrableOn_Iic_iff_integrableOn_Iio'proof · cited by 1
- Set.mem_Iic_Iio_of_subset_of_subsetproof · cited by 1