Theorems · Theorem · general topology
dist_triangle4_right
∀ {α : Type u} [inst : PseudoMetricSpace α] (x₁ y₁ x₂ y₂ : α), dist x₁ y₁ ≤ dist x₁ x₂ + dist y₁ y₂ + dist x₂ y₂- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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 and proof · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- dist_commproof · cited by 188
- add_right_commproof · cited by 85
- dist_triangle4proof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- dist_le_of_approx_trajectories_ODE_of_memproof · cited by 2
- BoundedContinuousFunction.arzela_ascoli₁proof · cited by 1
- ContractingWith.dist_inequalityproof · cited by 1