Theorems · Theorem · functional analysis
ediam_smul_le
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : SeminormedAddCommGroup 𝕜] [inst_1 : SeminormedAddCommGroup E]
[inst_2 : SMulZeroClass 𝕜 E] [IsBoundedSMul 𝕜 E] (c : 𝕜) (s : Set E), Metric.ediam (c • s) ≤ ‖c‖₊ • Metric.ediam s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENNRealstatement · cited by 9,879
- NNRealstatement · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNNorm.nnnormstatement · cited by 952
- Set.smulSetstatement · cited by 608
- IsBoundedSMulstatement and proof · cited by 329
- SMulZeroClassstatement and proof · cited by 213
- Metric.ediamstatement · cited by 159
- lipschitzWith_smulproof · cited by 5
- LipschitzWith.ediam_image_leproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- ediam_smul₀proof · cited by 1