Theorems · Theorem · convex and discrete geometry
ProperCone.innerDual_sUnion
∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : CompleteSpace E]
(S : Set (Set E)), ProperCone.innerDual (⋃₀ S) = sInf (ProperCone.innerDual '' S)- 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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Cites13
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
- Set.imagestatement · cited by 5,609
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- Inner.innerproof · cited by 1,089
- InfSet.sInfstatement · cited by 935
- Set.sUnionstatement · cited by 392
- ClosedSubmoduleproof · cited by 123
- ProperConestatement · cited by 57
- ProperCone.innerDualstatement and proof · cited by 15
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