Theorems · Theorem · order theory
Finset.mem_Iio
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : LocallyFiniteOrderBot α] {a x : α}, x ∈ Finset.Iio a ↔ x < a- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Finset.Iiostatement · cited by 147
- LocallyFiniteOrderBot.finset_mem_Iioproof · cited by 1
Cited by20
Results whose statement or proof uses this declaration.
- Finset.coe_Iioproof · cited by 34
- InnerProductSpace.gramSchmidt_orthogonalproof · cited by 6
- Finset.notMem_Iio_selfproof · cited by 6
- InnerProductSpace.mem_span_gramSchmidtproof · cited by 4
- Finset.disjoint_Ioi_Iioproof · cited by 3
- InnerProductSpace.gramSchmidt_ne_zero_coeproof · cited by 2
- Finset.sum_Iio_add_zero_commproof · cited by 2
- Set.toFinset_Iioproof · cited by 2
- disjoint_disjointed_of_ltproof · cited by 1
- Finset.sum_Iic_add_zero_commproof · cited by 1
- InnerProductSpace.gramSchmidt_of_orthogonalproof · cited by 1
- Fin.map_valEmbedding_Iioproof · cited by 1