Theorems · Theorem · order theory
LowerSet.Iic_sInf
∀ {α : Type u_1} [inst : CompleteLattice α] (S : Set α), LowerSet.Iic (sInf S) = ⨅ a ∈ S, LowerSet.Iic a- Defined in
- Mathlib.Order.UpperLower.Principal
- Cited by
- 0 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- InfSet.sInfstatement · cited by 935
- LowerSetstatement · cited by 230
- SetLike.extproof · cited by 92
- LowerSet.Iicstatement · cited by 37
- le_sInf_iffproof · cited by 13
- LowerSet.mem_Iic_iffproof · cited by 3
- LowerSet.mem_iInf_iffproof · cited by 3
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