Theorems · Theorem · convex and discrete geometry
ProperCone.innerDual_univ
∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : CompleteSpace E],
ProperCone.innerDual Set.univ = ⊥Dual cone of the total space is the convex cone {0}.
- Defined in
- Mathlib.Analysis.Convex.Cone.InnerDual
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Norm.normproof · cited by 5,413
- Bot.botstatement · cited by 4,720
- Set.univstatement and proof · cited by 3,945
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- le_antisymmproof · cited by 2,068
- Set.mem_univproof · cited by 416
- map_negproof · cited by 378
- ClosedSubmodulestatement · cited by 123
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