Theorems · Definition · order theory
Set.Iic
{α : Type u_1} → [Preorder α] → α → Set αIic b is the left-infinite right-closed interval $(-∞, b]$.
- Defined in
- Mathlib.Order.Interval.Set.Defs
- Cited by
- 1,111 results in Mathlib
- Foundations
- Depth 2 from the axioms, rests on 7 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.ofPredproof · cited by 6,101
Cited by1,191
Results whose statement or proof uses this declaration.
- Filter.atBotproof · cited by 512
- MeasureTheory.IsStronglyProgressiveproof · cited by 54
- Ordinal.logproof · cited by 45
- Set.mem_Iicstatement · cited by 37
- interior_Iccproof · cited by 37
- LowerSet.Iicproof · cited by 37
- Finset.coe_Iicstatement · cited by 36
- Set.self_mem_Iicstatement · cited by 26
- Set.Iic_subset_Iicstatement and proof · cited by 25
- CategoryTheory.SmallObject.SuccStruct.Iteration.Fstatement · cited by 23
- isClosed_Iicstatement · cited by 23
- MeasureTheory.lowerCrossingTimeproof · cited by 23
Showing the 200 most cited of 1,191.