Theorems · Theorem · functional analysis
egauge_zero_right
∀ (𝕜 : Type u_1) [inst : NormedDivisionRing 𝕜] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{s : Set E}, s.Nonempty → egauge 𝕜 s 0 = 0- Defined in
- Mathlib.Analysis.Convex.EGauge
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.Nonemptystatement and proof · cited by 2,627
- NormedDivisionRingstatement and proof · cited by 360
- SMulWithZeroproof · cited by 113
- egaugestatement and proof · cited by 75
- enorm_zeroproof · cited by 44
- Set.zero_smul_setproof · cited by 20
- egauge_le_of_mem_smulproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- Asymptotics.IsLittleOTVS.zeroproof · cited by 5
- egauge_smul_rightproof · cited by 1
- Asymptotics.IsLittleOTVS.tendsto_inv_smulproof · cited by 1
- egauge_zero_zeroproof · cited by 0