Theorems · Theorem · functional analysis
one_le_gauge_of_notMem
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s : Set E} {x : E},
StarConvex ℝ 0 s → Absorbs ℝ s {x} → x ∉ s → 1 ≤ gauge s x- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 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.
Cites9
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
- one_smulproof · cited by 1,374
- gaugestatement · cited by 85
- StarConvexstatement and proof · cited by 62
- Absorbsstatement and proof · cited by 59
- le_gauge_of_notMemproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- separate_convex_open_setproof · cited by 2