Theorems · Theorem · general topology
IsUltrametricDist.norm_tsum_le
∀ {M : Type u_1} {ι : Type u_2} [inst : SeminormedAddCommGroup M] [IsUltrametricDist M] (f : ι → M),
‖∑' (i : ι), f i‖ ≤ ⨆ i, ‖f i‖- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
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
- Finsetproof · cited by 13,712
- Norm.normstatement and proof · cited by 5,413
- Set.rangeproof · cited by 4,705
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- iSupstatement and proof · cited by 2,415
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- le_reflproof · cited by 2,061
- tsumstatement · cited by 1,148
- Summableproof · cited by 778
- IsEmptyproof · cited by 759
- norm_nonnegproof · cited by 725
Cited by2
Results whose statement or proof uses this declaration.
- IsUltrametricDist.nnnorm_tsum_leproof · cited by 1
- IsUltrametricDist.norm_tsum_le_of_forall_leproof · cited by 1