Theorems · Theorem · order theory
Set.nonempty_Ici
∀ {α : Type u_1} [inst : Preorder α] {a : α}, (Set.Ici a).Nonempty- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Set.Nonemptystatement · cited by 2,627
- Set.Icistatement · cited by 1,070
- Set.self_mem_Iciproof · cited by 30
Cited by9
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_mono_measureproof · cited by 5
- UpperSet.Ici_ne_topproof · cited by 4
- isCofinal_setOfPred_imp_ltproof · cited by 2
- isConnected_Iciproof · cited by 2
- not_bddAbove_Iciproof · cited by 1
- MeasureTheory.measure_iInter_eq_iInf_measure_iInter_leproof · cited by 1
- SimpleGraph.eventually_isContained_of_card_edgeFinsetproof · cited by 1
- Real.isGLB_of_tendsto_antitoneOn_bddBelow_nat_Iciproof · cited by 1
- Real.isLUB_of_tendsto_monotoneOn_bddAbove_nat_Iciproof · cited by 0