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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
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Foundations
Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedDivisionRingAddCommGroupModule

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