Theorems · Theorem · order theory
CovBy.Iio_eq
∀ {α : Type u_1} [inst : LinearOrder α] {a b : α}, a ⋖ b → Set.Iio b = Set.Iic a- Defined in
- Mathlib.Order.Cover
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrder
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
- LinearOrderstatement and proof · cited by 8,572
- Set.Iiostatement · cited by 1,166
- Set.Iicstatement and proof · cited by 1,111
- CovBystatement and proof · cited by 290
- Set.union_emptyproof · cited by 78
- CovBy.ltproof · cited by 51
- CovBy.Ioo_eqproof · cited by 6
- Set.Iic_union_Ioo_eq_Iioproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- PredOrder.isOpen_singleton_of_not_isPredPrelimitproof · cited by 1
- Order.isLUB_Iio_iff_isSuccPrelimitproof · cited by 0