Theorems · Theorem · convex and discrete geometry
mem_Icc_of_mem_stdSimplex
∀ {𝕜 : Type u_2} {ι : Type u_1} [inst : Semiring 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : Fintype ι]
[IsOrderedAddMonoid 𝕜] {f : ι → 𝕜}, f ∈ stdSimplex 𝕜 ι → ∀ (x : ι), f x ∈ Set.Icc 0 1All values of a function f ∈ stdSimplex 𝕜 ι belong to [0, 1].
- Defined in
- Mathlib.Analysis.Convex.StdSimplex
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Setstatement · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Fintypestatement and proof · cited by 7,736
- PartialOrderstatement and proof · cited by 6,410
- Finset.univproof · cited by 3,473
- Set.Iccstatement · cited by 1,702
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- Finset.mem_univproof · cited by 361
- stdSimplexstatement and proof · cited by 76
- Finset.single_le_sumproof · cited by 34
Cited by3
Results whose statement or proof uses this declaration.
- stdSimplex_subset_Iccproof · cited by 1
- stdSimplex_subset_closedBallproof · cited by 1
- diam_stdSimplex_leproof · cited by 1