Theorems · Inductive type · general topology
IsUltrametricDist
(X : Type u_2) → [Dist X] → Prop
The dist : X → X → ℝ respects the ultrametric inequality
of dist(x, z) ≤ max (dist(x,y)) (dist(y,z)).
- Defined in
- Mathlib.Topology.MetricSpace.Ultra.Basic
- Cited by
- 177 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- Dist
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Diststatement · cited by 35
Cited by207
Results whose statement or proof uses this declaration.
- NormedField.toValuedstatement and proof · cited by 14
- spectralAlgNormstatement and proof · cited by 9
- IsUltrametricDist.dist_triangle_maxstatement and proof · cited by 8
- IsUltrametricDist.isNonarchimedean_normstatement and proof · cited by 8
- IsUltrametricDist.algNormOfAlgEquivstatement and proof · cited by 7
- IsUltrametricDist.norm_add_le_maxstatement and proof · cited by 7
- PadicInt.addChar_of_value_at_onestatement and proof · cited by 7
- NormedField.valuationstatement and proof · cited by 6
- IsUltrametricDist.invariantExtensionstatement and proof · cited by 6
- spectralMulAlgNormstatement and proof · cited by 5
- Finset.Nonempty.norm_sum_le_sup'_normstatement and proof · cited by 4
- spectralAlgNorm_of_finiteDimensional_normalstatement and proof · cited by 4
Showing the 200 most cited of 207.