Theorems · Theorem · functional analysis
Seminorm.ball_smul_ball
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
(p : Seminorm 𝕜 E) (r₁ r₂ : ℝ), Metric.ball 0 r₁ • p.ball 0 r₂ ⊆ p.ball 0 (r₁ * r₂)- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- LE.le.transproof · cited by 3,151
- MulZeroClass.mul_zeroproof · cited by 2,091
- eq_or_neproof · cited by 1,117
- Metric.ballstatement and proof · cited by 735
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
- Set.smulstatement · cited by 110
- Seminorm.ballstatement and proof · cited by 78
Cited by1
Results whose statement or proof uses this declaration.
- SeminormFamily.basisSets_smulproof · cited by 0