Theorems · Theorem · order theory
iSupIndep.iInf
∀ {α : Type u_2} [inst : CompleteLattice α] [IsModularLattice α] [IsCompactlyGenerated α] {ι : Type u_3}
{κ : ι → Type u_4} (f : (i : ι) → κ i → α), (∀ (i : ι), iSupIndep (f i)) → iSupIndep fun k => ⨅ i, f i (k i)If each family f i is iSupIndep, then the family of pointwise infima
k ↦ ⨅ i, f i (k i) is also iSupIndep.
- Defined in
- Mathlib.Order.CompactlyGenerated.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- IsModularLatticestatement and proof · cited by 86
- Finset.SupIndepproof · cited by 52
- Function.ne_iffproof · cited by 40
- IsCompactlyGeneratedstatement and proof · cited by 37
- Finset.strongInductionproof · cited by 10
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