Theorems · Theorem · convex and discrete geometry
starConvex_compl_Ici
∀ {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 x (Set.Ici y)ᶜIf x < y, then (Set.Ici y)ᶜ is star convex at x.
- Defined in
- Mathlib.Analysis.Convex.Star
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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 · cited by 2,925
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Set.Icistatement · cited by 1,070
- IsStrictOrderedModulestatement and proof · cited by 111
- StarConvexstatement · cited by 62
- PosSMulReflectLTstatement and proof · cited by 28
- starConvex_compl_Iicproof · cited by 2
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