Theorems · Theorem · general topology
IsUltrametricDist.nnnorm_zsmul_le
∀ {S : Type u_1} [inst : SeminormedAddGroup S] [IsUltrametricDist S] (x : S) (z : ℤ), ‖z • x‖₊ ≤ ‖x‖₊- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 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.
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement and proof · cited by 952
- SeminormedAddGroupstatement and proof · cited by 331
- IsUltrametricDiststatement and proof · cited by 177
- natCast_zsmulproof · cited by 118
- negSucc_zsmulproof · cited by 45
- nnnorm_negproof · cited by 13
- IsUltrametricDist.nnnorm_nsmul_leproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- IsUltrametricDist.norm_zsmul_leproof · cited by 1