Theorems · Theorem · convex and discrete geometry
stdSimplex_subset_closedBall
∀ {ι : Type u_1} [inst : Fintype ι], stdSimplex ℝ ι ⊆ Metric.closedBall 0 1Every vector in stdSimplex 𝕜 ι has max-norm at most 1.
- Defined in
- Mathlib.Analysis.Convex.StdSimplex
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Dist.distproof · cited by 1,539
- Metric.closedBallstatement · cited by 704
- zero_le_oneproof · cited by 316
- abs_of_nonnegproof · cited by 279
- stdSimplexstatement and proof · cited by 76
- Pi.zero_applyproof · cited by 70
- Metric.mem_closedBallproof · cited by 42
- dist_pi_le_iffproof · cited by 10
- mem_Icc_of_mem_stdSimplexproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- bounded_stdSimplexproof · cited by 1