Theorems · Theorem · functional analysis
egauge_anti
∀ (𝕜 : Type u_1) [inst : NNNorm 𝕜] {E : Type u_2} [inst_1 : SMul 𝕜 E] {s t : Set E},
s ⊆ t → ∀ (x : E), egauge 𝕜 t x ≤ egauge 𝕜 s x- Defined in
- Mathlib.Analysis.Convex.EGauge
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- egaugestatement · cited by 75
- NNNormstatement and proof · cited by 33
- MulActionHom.idproof · cited by 8
- Set.MapsTo.egauge_leproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Filter.HasBasis.isBigOTVS_iffproof · cited by 5
- div_le_egauge_ballproof · cited by 4
- Filter.HasBasis.isLittleOTVS_iffproof · cited by 4
- Asymptotics.isLittleOTVS_iff_smallSetsproof · cited by 1
- Asymptotics.isBigOTVS_iff_smallSetsproof · cited by 1
- le_egauge_interproof · cited by 0