Theorems · Theorem · general topology
IsUltrametricDist.norm_add_le_max
∀ {S : Type u_1} [inst : SeminormedAddGroup S] [IsUltrametricDist S] (x y : S), ‖x + y‖ ≤ max ‖x‖ ‖y‖- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- neg_negproof · cited by 960
- neg_zeroproof · cited by 542
- SeminormedAddGroupstatement and proof · cited by 331
- IsUltrametricDiststatement and proof · cited by 177
- dist_eq_norm_neg_addproof · cited by 46
- IsUltrametricDist.dist_triangle_maxproof · cited by 8
- le_sup_iffproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- Finset.Nonempty.norm_sum_le_sup'_normproof · cited by 4
- IsUltrametricDist.norm_add_one_le_max_norm_oneproof · cited by 1
- IsUltrametricDist.nnnorm_add_le_maxproof · cited by 1
- PadicComplex.isNonarchimedeanproof · cited by 0
- PadicInt.norm_ascPochhammer_leproof · cited by 0
- IsUltrametricDist.exists_norm_multiset_sum_leproof · cited by 0
- IsKrasner.of_completeSpace_of_normalproof · cited by 0