Theorems · Theorem · order theory
LowerSet.Iic_iInf
∀ {α : Type u_1} {ι : Sort u_3} [inst : CompleteLattice α] (f : ι → α),
LowerSet.Iic (⨅ i, f i) = ⨅ i, LowerSet.Iic (f i)- Defined in
- Mathlib.Order.UpperLower.Principal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- LowerSetstatement · cited by 230
- SetLike.extproof · cited by 92
- LowerSet.Iicstatement · cited by 37
- le_iInf_iffproof · cited by 30
- LowerSet.mem_Iic_iffproof · cited by 3
- LowerSet.mem_iInf_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- LowerSet.Iic_iInf₂proof · cited by 0