Theorems · Theorem · functional analysis
mul_gauge_le_norm
∀ {E : Type u_2} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {s : Set E} {r : ℝ} {x : E},
Metric.ball 0 r ⊆ s → r * gauge s x ≤ ‖x‖- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- mul_commproof · cited by 2,262
- LT.lt.leproof · cited by 2,189
- Metric.ballstatement and proof · cited by 735
- norm_nonnegproof · cited by 725
- le_or_gtproof · cited by 269
- gaugestatement and proof · cited by 85
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