Theorems · Theorem · order theory
Finset.sup_Iic
∀ {α : Type u_2} [inst : SemilatticeSup α] [inst_1 : LocallyFiniteOrderBot α] [inst_2 : OrderBot α] (a : α),
(Finset.Iic a).sup id = a- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 4 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- Finset.supstatement · cited by 530
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Finset.Iicstatement · cited by 280
- Finset.le_supproof · cited by 112
- Finset.sup_leproof · cited by 44
- Finset.mem_Iicproof · cited by 42
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.inducedFamily_Iicproof · cited by 3
- Finset.sum_eq_sum_range_sdiffproof · cited by 1
- Finset.prod_eq_prod_range_sdiffproof · cited by 0
- OrderIso.supIrredLowerSet_symm_applyproof · cited by 0