Theorems · Theorem · order theory
Set.Iio_zero_eq_empty
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : Zero α] [IsBotZeroClass α], Set.Iio 0 = ∅- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
- Assumes
- PreorderZeroIsBotZeroClass
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 · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.extproof · cited by 2,266
- Set.Iiostatement · cited by 1,166
- IsBotZeroClassstatement and proof · cited by 71
- Set.mem_Iioproof · cited by 49
- Set.mem_empty_iff_falseproof · cited by 32
- not_lt_zeroproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Fin.isAddFreimanIso_Iioproof · cited by 3