Theorems · Theorem · order theory
CovBy.Ico_eq
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, a ⋖ b → Set.Ico a b = {a}- Defined in
- Mathlib.Order.Cover
- Cited by
- 3 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.Icostatement · cited by 799
- CovBystatement and proof · cited by 290
- Set.empty_unionproof · cited by 52
- CovBy.ltproof · cited by 51
- CovBy.Ioo_eqproof · cited by 6
- Set.Ioo_union_leftproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- PredOrder.isOpen_singleton_of_not_isPredPrelimitproof · cited by 1
- Set.Ico_eq_singleton_iffproof · cited by 0
- Set.Ioo_eq_singleton_iffproof · cited by 0