Theorems · Theorem · order theory
LowerSet.compl_sInf
∀ {α : Type u_1} [inst : LE α] (S : Set (LowerSet α)), (sInf S).compl = ⨅ s ∈ S, s.compl- Defined in
- Mathlib.Order.UpperLower.CompleteLattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LE
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Cites12
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
- SetLike.coeproof · cited by 8,199
- Compl.complproof · cited by 2,925
- Set.iUnionproof · cited by 2,483
- iInfstatement · cited by 1,690
- InfSet.sInfstatement · cited by 935
- UpperSetstatement · cited by 245
- LowerSetstatement and proof · cited by 230
- UpperSet.extproof · cited by 29
- LowerSet.complstatement and proof · cited by 17
- Set.compl_iInter₂proof · cited by 5
- UpperSet.coe_iInf₂proof · cited by 3
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