Theorems · Theorem · functional analysis
mem_of_egauge_lt_one
∀ {𝕜 : Type u_1} [inst : NormedDivisionRing 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{s : Set E} {x : E}, Balanced 𝕜 s → egauge 𝕜 s x < 1 → x ∈ s- Defined in
- Mathlib.Analysis.Convex.EGauge
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- ENNRealstatement · cited by 9,879
- one_smulproof · cited by 1,374
- NormedDivisionRingstatement and proof · cited by 360
- Balancedstatement and proof · cited by 77
- egaugestatement and proof · cited by 75
- enorm_oneproof · cited by 26
- mem_smul_of_egauge_ltproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleOTVS_oneproof · cited by 4