Theorems · Theorem · functional analysis
div_le_egauge_closedBall
∀ (𝕜 : Type u_1) [inst : NormedField 𝕜] {E : Type u_2} [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E]
(r : NNReal) (x : E), ‖x‖ₑ / ↑r ≤ egauge 𝕜 (Metric.closedBall 0 ↑r) x- Defined in
- Mathlib.Analysis.Convex.EGauge
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- ENNRealstatement and proof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- le_reflproof · cited by 2,061
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- NNReal.toRealstatement and proof · cited by 1,260
- NormedFieldstatement and proof · cited by 1,084
- ENorm.enormstatement and proof · cited by 715
- Metric.closedBallstatement and proof · cited by 704
- mul_le_mul'proof · cited by 274
Cited by2
Results whose statement or proof uses this declaration.
- div_le_egauge_ballproof · cited by 4
- le_egauge_closedBall_oneproof · cited by 0