Theorems · Theorem · order theory
Set.Iic_subset_Iic
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, Set.Iic a ⊆ Set.Iic b ↔ a ≤ b- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 25 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.
Cites5
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
- LE.le.transproof · cited by 3,151
- Set.Iicstatement and proof · cited by 1,111
- Set.self_mem_Iciproof · cited by 30
Cited by25
Results whose statement or proof uses this declaration.
- IsCompact.exists_isLeastproof · cited by 9
- Metric.cthickening_monoproof · cited by 6
- LowerSemicontinuousOn.exists_isMinOnproof · cited by 6
- monotone_Iicproof · cited by 5
- IsBot.atBot_eqproof · cited by 3
- StrictMonoOn.Iic_id_leproof · cited by 3
- ProbabilityTheory.setLIntegral_stieltjesOfMeasurableRatproof · cited by 2
- ProbabilityTheory.setLIntegral_toKernel_univproof · cited by 2
- MonotoneOn.exists_monotone_extensionproof · cited by 2
- MeasureTheory.Measure.ext_of_Iicproof · cited by 2
- Iic_mem_nhdsSet_Iic_iffproof · cited by 1
- SequentiallyComplete.setSeq_monoproof · cited by 1