Theorems · Theorem · general topology
IsUltrametricDist.norm_div_eq_max_of_norm_div_ne_norm_div
∀ {S : Type u_1} [inst : SeminormedGroup S] [IsUltrametricDist S] (x y z : S),
‖x / y‖ ≠ ‖y / z‖ → ‖x / z‖ = max ‖x / y‖ ‖y / z‖All triangles are isosceles in an ultrametric normed group.
- Defined in
- Mathlib.Analysis.Normed.Group.Ultra
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SeminormedGroupstatement and proof · cited by 250
- IsUltrametricDiststatement and proof · cited by 177
- div_mul_div_cancelproof · cited by 13
- IsUltrametricDist.norm_mul_eq_max_of_norm_ne_normproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsUltrametricDist.nnnorm_div_eq_max_of_nnnorm_div_ne_nnnorm_divproof · cited by 0