Theorems · Theorem · functional analysis
Seminorm.ball_norm_mul_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}, p.ball 0 (‖k‖ * r) ⊆ k • p.ball 0 r- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
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- 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
- Norm.normstatement and proof · cited by 5,413
- one_mulproof · cited by 2,841
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- MulZeroClass.zero_mulproof · cited by 1,625
- le_rflproof · cited by 1,558
- one_smulproof · cited by 1,374
- eq_or_neproof · cited by 1,117
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