Theorems · Theorem · convex and discrete geometry
diam_stdSimplex_le
∀ {ι : Type u_1} [inst : Fintype ι], Metric.diam (stdSimplex ℝ ι) ≤ 1The (sup metric) diameter of a standard simplex is less than or equal to 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Set.Iccproof · cited by 1,702
- zero_le_oneproof · cited by 316
- stdSimplexstatement and proof · cited by 76
- Metric.diamstatement · cited by 74
- dist_pi_le_iffproof · cited by 10
- Metric.diam_le_of_forall_dist_leproof · cited by 5
- mem_Icc_of_mem_stdSimplexproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- diam_stdSimplexproof · cited by 0