Theorems · Theorem · convex and discrete geometry
diam_stdSimplex
∀ {ι : Type u_1} [inst : Fintype ι] [Nontrivial ι], Metric.diam (stdSimplex ℝ ι) = 1The (sup metric) diameter of a standard simplex indexed by a nontrivial index is 1.
- Defined in
- Mathlib.Analysis.Convex.StdSimplex
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeNontrivial
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Cites18
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
- Nontrivialstatement and proof · cited by 2,416
- le_antisymmproof · cited by 2,068
- absproof · cited by 1,814
- Dist.distproof · cited by 1,539
- sub_zeroproof · cited by 938
- Pi.singleproof · cited by 518
- abs_oneproof · cited by 87
- stdSimplexstatement and proof · cited by 76
- Metric.diamstatement and proof · cited by 74
- max_selfproof · cited by 43
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