Theorems · Theorem · functional analysis
Seminorm.vadd_ball
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : SMul 𝕜 E] {x y : E}
{r : ℝ} (p : Seminorm 𝕜 E), x +ᵥ p.ball y r = p.ball (x +ᵥ y) rThe image of a ball under addition with a singleton is another ball.
- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- AddCommGroupstatement and proof · cited by 12,871
- SeminormedAddCommGroupproof · cited by 2,671
- HVAdd.hVAddstatement and proof · cited by 1,820
- Metric.ballproof · cited by 735
- SeminormedRingstatement and proof · cited by 446
- Set.vaddSetstatement · cited by 403
- Seminormstatement and proof · cited by 272
- Seminorm.ballstatement · cited by 78
- Seminorm.toAddGroupSeminormproof · cited by 10
- AddGroupSeminorm.toSeminormedAddCommGroupproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- WithSeminorms.hasBasis_ballproof · cited by 2