Theorems · Theorem · convex and discrete geometry
diam_stdSimplex_of_subsingleton
∀ {ι : Type u_1} [inst : Fintype ι] [Subsingleton ι], Metric.diam (stdSimplex ℝ ι) = 0The (sup metric) diameter of a standard simplex indexed by a subsingleton is 0.
- Defined in
- Mathlib.Analysis.Convex.StdSimplex
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeSubsingleton
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- IsEmptyproof · cited by 759
- isEmpty_or_nonemptyproof · cited by 269
- stdSimplexstatement · cited by 76
- Metric.diamstatement and proof · cited by 74
- Metric.diam_singletonproof · cited by 3
- Metric.diam_emptyproof · cited by 3
- stdSimplex_of_isEmpty_indexproof · cited by 1
- stdSimplex_uniqueproof · cited by 1
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