Theorems · Theorem · order theory
Finset.nonempty_Iic
∀ {α : Type u_2} {a : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrderBot α], (Finset.Iic a).Nonempty- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- le_rflproof · cited by 1,558
- Finset.Nonemptystatement · cited by 1,001
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Finset.Iicstatement · cited by 280
- Finset.mem_Iicproof · cited by 42
Cited by19
Results whose statement or proof uses this declaration.
- partialSupsproof · cited by 67
- partialSups_applystatement · cited by 7
- partialSups_disjointedproof · cited by 5
- disjointed_succproof · cited by 3
- partialSups_iff_forallproof · cited by 3
- partialSups_succproof · cited by 3
- partialSups_botproof · cited by 2
- Finset.disjiUnion_Iic_disjointedproof · cited by 2
- partialSups_eq_ciSup_Iicproof · cited by 2
- MeasureTheory.IsSetRing.partialSups_memproof · cited by 1
- disjointed_partialSupsproof · cited by 1
- Monotone.disjointed_succ_supproof · cited by 1