Theorems · Theorem · functional analysis
le_gauge_of_notMem
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} {x : E} {a : ℝ},
StarConvex ℝ 0 s → Absorbs ℝ s {x} → x ∉ a • s → a ≤ gauge s x- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredproof · cited by 6,101
- Norm.normproof · cited by 5,413
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- le_of_ltproof · cited by 1,175
- Set.smulSetstatement · cited by 608
- Eq.geproof · cited by 375
- mul_posproof · cited by 374
Cited by1
Results whose statement or proof uses this declaration.
- one_le_gauge_of_notMemproof · cited by 1