Theorems · Theorem · order theory
Set.Iio_insert
∀ {α : Type u_1} [inst : PartialOrder α] {a : α}, insert a (Set.Iio a) = Set.Iic a- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 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_eq_or_ltproof · cited by 20
Cited by5
Results whose statement or proof uses this declaration.
- Cardinal.mk_Iic_ltproof · cited by 2
- PredOrder.nhdsLEproof · cited by 1
- nhdsLT_sup_nhdsWithin_singletonproof · cited by 0
- Field.Emb.Cardinal.filtration_succproof · cited by 0
- CovBy.nhdsLEproof · cited by 0