Theorems · Theorem · order theory
Finset.disjoint_Ioi_Iio
∀ {α : Type u_2} [inst : Preorder α] [inst_1 : LocallyFiniteOrderTop α] [inst_2 : LocallyFiniteOrderBot α] (a : α),
Disjoint (Finset.Ioi a) (Finset.Iio a)- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Preorderstatement and proof · cited by 7,952
- Disjointstatement · cited by 2,201
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Finset.Iiostatement and proof · cited by 147
- LocallyFiniteOrderTopstatement and proof · cited by 114
- Finset.Ioistatement and proof · cited by 106
- LT.lt.not_gtproof · cited by 54
- Finset.disjoint_leftproof · cited by 50
- Finset.mem_Iioproof · cited by 20
- Finset.mem_Ioiproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- Finset.Ioi_disjUnion_Iiostatement and proof · cited by 1
- Finset.prod_prod_Ioi_mul_eq_prod_prod_off_diagproof · cited by 1
- Finset.sum_sum_Ioi_add_eq_sum_sum_off_diagproof · cited by 0