Theorems · Theorem · functional analysis
egauge_le_of_mem_smul
∀ {𝕜 : Type u_1} [inst : NNNorm 𝕜] {E : Type u_2} [inst_1 : SMul 𝕜 E] {c : 𝕜} {s : Set E} {x : E},
x ∈ c • s → egauge 𝕜 s x ≤ ‖c‖ₑ- Defined in
- Mathlib.Analysis.Convex.EGauge
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- ENorm.enormstatement · cited by 715
- Set.smulSetstatement · cited by 608
- egaugestatement · cited by 75
- iInf₂_leproof · cited by 45
- NNNormstatement and proof · cited by 33
Cited by7
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleOTVS_oneproof · cited by 4
- egauge_zero_rightproof · cited by 4
- egauge_le_of_smul_mem_of_neproof · cited by 2
- LinearMap.isBigOTVS_rev_compproof · cited by 2
- egauge_le_oneproof · cited by 1
- le_egauge_smul_leftproof · cited by 1
- le_egauge_smul_rightproof · cited by 1