Theorems · Theorem · general topology
IsUltrametricDist.nnnorm_tprod_le
∀ {M : Type u_1} {ι : Type u_2} [inst : SeminormedCommGroup M] [IsUltrametricDist M] (f : ι → M),
‖∏' (i : ι), f i‖₊ ≤ ⨆ i, ‖f i‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Norm.normproof · cited by 5,413
- NNRealstatement · cited by 4,310
- iSupstatement · cited by 2,415
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- NNNorm.nnnormstatement and proof · cited by 952
- tprodstatement and proof · cited by 230
- SeminormedCommGroupstatement and proof · cited by 191
- IsUltrametricDiststatement and proof · cited by 177
- NNReal.coe_iSupproof · cited by 8
- IsUltrametricDist.norm_tprod_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsUltrametricDist.nnnorm_tprod_le_of_forall_leproof · cited by 0