Theorems · Theorem · order theory
Finset.Ici_eq_cons_Ioi
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : LocallyFiniteOrderTop α] (a : α),
Finset.Ici a = Finset.cons a (Finset.Ioi a) ⋯Finset.cons version of Finset.Ioi_insert.
- 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- PartialOrderstatement and proof · cited by 6,410
- Finset.consstatement · cited by 221
- LocallyFiniteOrderTopstatement and proof · cited by 114
- Finset.Ioistatement and proof · cited by 106
- Finset.Icistatement and proof · cited by 105
- Finset.cons_eq_insertproof · cited by 59
- Finset.notMem_Ioi_selfstatement and proof · cited by 4
- Finset.Ioi_insertproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Finset.card_Ioi_eq_card_Ici_sub_oneproof · cited by 1
- Finset.add_sum_Ioi_eq_sum_Iciproof · cited by 1
- Finset.mul_prod_Ioi_eq_prod_Iciproof · cited by 1