Theorems · Theorem · convex and discrete geometry
ProperCone.innerDual_innerDual
∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : CompleteSpace E]
(C : ProperCone ℝ E), ProperCone.innerDual ↑(ProperCone.innerDual ↑C) = CThe inner dual of inner dual of a proper cone is itself.
- 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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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- SetLike.coestatement and proof · cited by 8,199
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- LinearMap.flipproof · cited by 193
- ProperConestatement and proof · cited by 57
- innerₗproof · cited by 23
- ProperCone.dualproof · cited by 16
- ProperCone.innerDualstatement · cited by 15
- flip_innerₗproof · cited by 4
- ProperCone.dual_flip_dualproof · cited by 2
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