Theorems · Theorem · functional analysis

Seminorm.ball_finset_sup_eq_iInter

∀ {𝕜 : Type u_3} {E : Type u_7} {ι : Type u_11} [inst : SeminormedRing 𝕜] [inst_1 : AddCommGroup E]
  [inst_2 : Module 𝕜 E] (p : ι → Seminorm 𝕜 E) (s : Finset ι) (x : E) {r : ℝ},
  0 < r → (s.sup p).ball x r = ⋂ i ∈ s, (p i).ball x r

Defined in

Mathlib.Analysis.Seminorm

Cited by

5 results in Mathlib

Foundations

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

Assumes

SeminormedRingAddCommGroupModule