Theorems · Theorem · functional analysis
le_egauge_smul_right
∀ {𝕜 : Type u_1} [inst : NormedDivisionRing 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] (c : 𝕜)
(s : Set E) (x : E), ‖c‖ₑ * egauge 𝕜 s x ≤ egauge 𝕜 s (c • x)- Defined in
- Mathlib.Analysis.Convex.EGauge
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- ENNRealstatement · cited by 9,879
- NNRealproof · cited by 4,310
- MulZeroClass.zero_mulproof · cited by 1,625
- MulActionproof · cited by 1,294
- ENNReal.ofNNRealproof · cited by 1,279
- eq_or_neproof · cited by 1,117
- le_transproof · cited by 985
- NNNorm.nnnormproof · cited by 952
- ENorm.enormstatement and proof · cited by 715
Cited by1
Results whose statement or proof uses this declaration.
- egauge_smul_rightproof · cited by 1