Theorems · Theorem · convex and discrete geometry
IsExposed.subset
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : TopologicalSpace 𝕜] [inst_1 : Ring 𝕜] [inst_2 : PartialOrder 𝕜]
[inst_3 : AddCommMonoid E] [inst_4 : TopologicalSpace E] [inst_5 : Module 𝕜 E] {A B : Set E}, IsExposed 𝕜 A B → B ⊆ A- Defined in
- Mathlib.Analysis.Convex.Exposed
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredproof · cited by 6,101
- StrongDualproof · cited by 459
- IsExposedstatement and proof · cited by 19
Cited by4
Results whose statement or proof uses this declaration.
- IsExposed.isExtremeproof · cited by 3
- IsExposed.inter_leftproof · cited by 1
- IsExposed.isCompactproof · cited by 1
- IsExposed.antisymmproof · cited by 0