Theorems · Theorem · functional analysis
PiTensorProduct.bddBelow_projectiveSemiNormAux
∀ {ι : Type u_1} [inst : Fintype ι] {𝕜 : Type u_2} {E : ι → Type u_3} [inst_1 : (i : ι) → SeminormedAddCommGroup (E i)]
[inst_2 : NormedField 𝕜] [inst_3 : (i : ι) → NormedSpace 𝕜 (E i)] (x : PiTensorProduct 𝕜 fun i => E i),
BddBelow (Set.range fun p => PiTensorProduct.projectiveSeminormAux ↑p)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement · cited by 7,166
- Set.rangestatement · cited by 4,705
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedFieldstatement and proof · cited by 1,084
- BddBelowstatement · cited by 401
- PiTensorProductstatement and proof · cited by 181
- FreeAddMonoidstatement and proof · cited by 145
- PiTensorProduct.liftsstatement and proof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- PiTensorProduct.projectiveSeminorm_tprod_leproof · cited by 2
- PiTensorProduct.projectiveSeminorm_smul_leproof · cited by 0
- PiTensorProduct.projectiveSeminorm_zeroproof · cited by 0
- PiTensorProduct.projectiveSeminorm_add_leproof · cited by 0