Theorems · Theorem · functional analysis
gauge_mono
∀ {E : Type u_2} [inst : AddCommGroup E] [inst_1 : Module ℝ E] {s t : Set E}, Absorbent ℝ s → s ⊆ t → gauge t ≤ gauge s- Defined in
- Mathlib.Analysis.Convex.Gauge
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 159 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 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
- gaugestatement · cited by 85
- Absorbentstatement and proof · cited by 60
- Set.mem_of_subset_of_memproof · cited by 48
- Set.ofPred_subset_ofPred_of_impproof · cited by 22
- Set.smul_set_monoproof · cited by 15
- csInf_le_csInfproof · cited by 9
- Absorbent.gauge_set_nonemptyproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- gauge_closedBallproof · cited by 1
- Convex.lipschitzWith_gaugeproof · cited by 1
- mul_gauge_le_normproof · cited by 0
- le_gauge_of_subset_closedBallproof · cited by 0