Theorems · Theorem · order theory
Finset.mem_Iic
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : LocallyFiniteOrderBot α] {a x : α}, x ∈ Finset.Iic a ↔ x ≤ a- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 42 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.Iicstatement · cited by 280
- LocallyFiniteOrderBot.finset_mem_Iicproof · cited by 1
Cited by42
Results whose statement or proof uses this declaration.
- Finset.coe_Iicproof · cited by 36
- Finset.nonempty_Iicproof · cited by 18
- sigPos_isGreatestproof · cited by 4
- Finset.sup_Iicproof · cited by 4
- Finset.subset_Iic_sup_idproof · cited by 4
- ProbabilityTheory.Kernel.partialTraj_eq_prodproof · cited by 3
- IicProdIoc_leproof · cited by 2
- Polynomial.Chebyshev.sumNodes_eq_sumNodes_T_iffproof · cited by 2
- Polynomial.Chebyshev.sumNodes_le_sumNodes_Tproof · cited by 2
- Fin.sum_sum_eq_sum_triangle_addproof · cited by 2
- ProbabilityTheory.Kernel.lmarginalPartialTraj_eq_lintegral_mapproof · cited by 2
- IicProdIoc_preimageproof · cited by 1