Theorems · Theorem · functional analysis
Seminorm.smul_closedBall_subset
∀ {𝕜 : Type u_3} {E : Type u_7} [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{p : Seminorm 𝕜 E} {k : 𝕜} {r : ℝ}, k • p.closedBall 0 r ⊆ p.closedBall 0 (‖k‖ * r)- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 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.
- DFunLike.coeproof · cited by 62,936
- 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
- Norm.normstatement and proof · cited by 5,413
- norm_nonnegproof · cited by 725
- Set.smulSetstatement · cited by 608
- mul_le_mul_of_nonneg_leftproof · cited by 361
- NormedDivisionRingstatement and proof · cited by 360
- Seminormstatement and proof · cited by 272
- Seminorm.closedBallstatement and proof · cited by 45
Cited by1
Results whose statement or proof uses this declaration.
- Seminorm.smul_closedBall_zeroproof · cited by 1