Theorems · Theorem · functional analysis
Seminorm.zero_or_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) (x : E), (s.sup p) x = 0 ∨ ∃ i ∈ s, (s.sup p) x = (p i) x- Defined in
- Mathlib.Analysis.Seminorm
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- Finsetstatement and proof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- Finset.Nonemptyproof · cited by 1,001
- Finset.supstatement and proof · cited by 530
- SeminormedRingstatement and proof · cited by 446
- Seminormstatement and proof · cited by 272
- Finset.eq_empty_or_nonemptyproof · cited by 104
- Seminorm.exists_apply_eq_finset_supproof · cited by 2
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