Theorems · Theorem · general topology
IsUltrametricDist.nnnorm_add_eq_max_of_nnnorm_ne_nnnorm
∀ {S : Type u_1} [inst : SeminormedAddGroup S] [IsUltrametricDist S] {x y : S}, ‖x‖₊ ≠ ‖y‖₊ → ‖x + y‖₊ = max ‖x‖₊ ‖y‖₊All triangles are isosceles in an ultrametric normed additive group.
- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 114 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.
- NNRealstatement · cited by 4,310
- NNReal.toRealproof · cited by 1,260
- NNNorm.nnnormstatement and proof · cited by 952
- SeminormedAddGroupstatement and proof · cited by 331
- IsUltrametricDiststatement and proof · cited by 177
- NNReal.coe_injproof · cited by 30
- NNReal.coe_injectiveproof · cited by 16
- NNReal.coe_maxproof · cited by 11
- IsUltrametricDist.norm_add_eq_max_of_norm_ne_normproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsUltrametricDist.nnnorm_sum_eq_sup_of_pairwise_neproof · cited by 1
- IsUltrametricDist.nnnorm_eq_of_add_nnnorm_lt_maxproof · cited by 0