Theorems · Theorem · functional analysis
pi_norm_le_iff_of_nonempty
∀ {ι : Type u_1} {G : ι → Type u_4} [inst : Fintype ι] [inst_1 : (i : ι) → SeminormedAddGroup (G i)] (f : (i : ι) → G i)
{r : ℝ} [Nonempty ι], ‖f‖ ≤ r ↔ ∀ (b : ι), ‖f b‖ ≤ r- Cited by
- 1 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- norm_nonnegproof · cited by 725
- SeminormedAddGroupstatement and proof · cited by 331
- Classical.arbitraryproof · cited by 161
- pi_norm_le_iff_of_nonnegproof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.fundamentalCone.isBounded_normLeOneproof · cited by 1