Theorems · Theorem · general topology
IsUltrametricDist.norm_add_eq_max_of_norm_ne_norm
∀ {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
- 3 results in Mathlib
- Foundations
- Depth 107 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 and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- neg_negproof · cited by 960
- SeminormedAddGroupstatement and proof · cited by 331
- norm_negproof · cited by 190
- IsUltrametricDiststatement and proof · cited by 177
- dist_zero_rightproof · cited by 172
- dist_eq_norm_neg_addproof · cited by 46
- dist_zeroproof · cited by 16
- dist_zero_leftproof · cited by 15
- IsUltrametricDist.dist_eq_max_of_dist_ne_distproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsUltrametricDist.nnnorm_add_eq_max_of_nnnorm_ne_nnnormproof · cited by 2
- IsUltrametricDist.norm_sub_eq_max_of_norm_sub_ne_norm_subproof · cited by 1
- IsUltrametricDist.norm_eq_of_add_norm_lt_maxproof · cited by 0