Theorems · Theorem · general topology
IsUltrametricDist.dist_triangle_max
∀ {X : Type u_2} {inst : Dist X} [self : IsUltrametricDist X] (x y z : X), dist x z ≤ max (dist x y) (dist y z)- Defined in
- Mathlib.Topology.MetricSpace.Ultra.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsUltrametricDist
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Dist.diststatement · cited by 1,539
- IsUltrametricDiststatement and proof · cited by 177
- Diststatement and proof · cited by 35
Cited by8
Results whose statement or proof uses this declaration.
- IsUltrametricDist.isNonarchimedean_normproof · cited by 8
- IsUltrametricDist.norm_add_le_maxproof · cited by 7
- IsUltrametricDist.norm_mul_le_maxproof · cited by 3
- IsUltrametricDist.closedBall_eq_of_memproof · cited by 3
- IsUltrametricDist.ball_eq_of_memproof · cited by 2
- IsUltrametricDist.dist_eq_max_of_dist_ne_distproof · cited by 2
- IsUltrametricDist.of_normedAlgebra'proof · cited by 1
- dist_triangle_maxproof · cited by 0