Theorems · Theorem · functional analysis

Seminorm.exists_apply_eq_finset_sup

∀ {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}, s.Nonempty → ∀ (x : E), ∃ i ∈ s, (s.sup p) x = (p i) x

Defined in

Mathlib.Analysis.Seminorm

Cited by

2 results in Mathlib

Foundations

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

Assumes

SeminormedRingAddCommGroupModule