Theorems · Theorem · convex and discrete geometry
ProperCone.mem_innerDual
∀ {E : Type u_2} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : CompleteSpace E] {s : Set E}
{y : E}, y ∈ ProperCone.innerDual s ↔ ∀ ⦃x : E⦄, x ∈ s → 0 ≤ inner ℝ x y- 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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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
- Inner.innerstatement · cited by 1,089
- ProperConestatement · cited by 57
- ProperCone.innerDualstatement · cited by 15
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