Theorems · Theorem · general topology
IsUltrametricDist.norm_tsum_le_of_forall_le
∀ {M : Type u_1} {ι : Type u_2} [inst : SeminormedAddCommGroup M] [IsUltrametricDist M] [Nonempty ι] {f : ι → M}
{C : ℝ}, (∀ (i : ι), ‖f i‖ ≤ C) → ‖∑' (i : ι), f i‖ ≤ C- 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.
Cites9
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
- Norm.normstatement and proof · cited by 5,413
- LE.le.transproof · cited by 3,151
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- IsUltrametricDiststatement and proof · cited by 177
- ciSup_leproof · cited by 56
- IsUltrametricDist.norm_tsum_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsUltrametricDist.norm_tsum_le_of_forall_le_of_nonnegproof · cited by 0