Theorems · Theorem · convex and discrete geometry
ProperCone.innerDual_iUnion
∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : CompleteSpace E]
{ι : Sort u_4} (f : ι → Set E), ProperCone.innerDual (⋃ i, f i) = ⨅ i, ProperCone.innerDual (f i)- Defined in
- Mathlib.Analysis.Convex.Cone.InnerDual
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
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
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- Set.iUnionstatement · cited by 2,483
- iInfstatement · cited by 1,690
- Inner.innerproof · cited by 1,089
- ProperConestatement · cited by 57
- ProperCone.innerDualstatement · cited by 15
- ProperCone.extproof · cited by 12
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