Theorems · Theorem · convex and discrete geometry
starConvex_compl_Iic
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : Ring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
[inst_3 : PartialOrder E] [IsOrderedAddMonoid E] [inst_5 : Module 𝕜 E] [IsStrictOrderedModule 𝕜 E]
[PosSMulReflectLT 𝕜 E] {x y : E}, x < y → StarConvex 𝕜 y (Set.Iic x)ᶜIf x < y, then (Set.Iic x)ᶜ is star convex at y.
- Defined in
- Mathlib.Analysis.Convex.Star
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Compl.complstatement and proof · cited by 2,925
- LT.lt.leproof · cited by 2,189
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- one_smulproof · cited by 1,374
- Set.Iicstatement and proof · cited by 1,111
- LT.lt.not_geproof · cited by 305
- add_smulproof · cited by 204
Cited by2
Results whose statement or proof uses this declaration.
- Complex.starConvex_slitPlaneproof · cited by 2
- starConvex_compl_Iciproof · cited by 0