Theorems · Theorem · convex and discrete geometry
ProperCone.hyperplane_separation_of_notMem
∀ {E : Type u_2} {F : Type u_3} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E]
[inst_2 : CompleteSpace E] [inst_3 : NormedAddCommGroup F] [inst_4 : InnerProductSpace ℝ F] [inst_5 : CompleteSpace F]
(K : ProperCone ℝ E) {f : E →L[ℝ] F} {b : F},
b ∉ ProperCone.map f K → ∃ y, (ContinuousLinearMap.adjoint f) y ∈ ProperCone.innerDual ↑K ∧ inner ℝ b y < 0- Defined in
- Mathlib.Analysis.Convex.Cone.InnerDual
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- SetLike.coestatement and proof · cited by 8,199
- ContinuousLinearMapstatement and proof · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- Inner.innerstatement and proof · cited by 1,089
- LinearIsometryEquivstatement · cited by 748
- starRingEndstatement · cited by 671
- ContinuousLinearMap.adjointstatement and proof · cited by 82
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.