Theorems · Theorem · functional analysis
gauge_empty
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E], gauge ∅ = 0- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 116 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- Set.Ioiproof · cited by 1,463
- InfSet.sInfproof · cited by 935
- gaugestatement · cited by 85
- Real.sInf_emptyproof · cited by 21
- gauge_def'proof · cited by 8
- Set.sep_falseproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- gauge_ballproof · cited by 3
- gauge_of_subset_zeroproof · cited by 1