Theorems · Theorem · order theory
Finset.Iic_eq_cons_Iio
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : LocallyFiniteOrderBot α] (b : α),
Finset.Iic b = Finset.cons b (Finset.Iio b) ⋯Finset.cons version of Finset.Iio_insert.
- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 5 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
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Finset.Iicstatement and proof · cited by 280
- Finset.consstatement · cited by 221
- Finset.Iiostatement and proof · cited by 147
- Finset.cons_eq_insertproof · cited by 59
- Finset.notMem_Iio_selfstatement and proof · cited by 6
- Finset.Iio_insertproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- partialSups_disjointedproof · cited by 5
- Finset.card_Iio_eq_card_Iic_sub_oneproof · cited by 3
- Finset.mul_prod_Iio_eq_prod_Iicproof · cited by 1
- Finset.add_sum_Iio_eq_sum_Iicproof · cited by 1
- disjointed_partialSupsproof · cited by 1