Theorems · Theorem · general topology
abs_dist_sub_le
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y z : α), |dist x z - dist y z| ≤ dist x y- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 106 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- absstatement · cited by 1,814
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- sub_le_iff_le_addproof · cited by 50
- dist_triangleproof · cited by 44
- abs_sub_le_iffproof · cited by 34
- dist_triangle_leftproof · cited by 11
Cited by8
Results whose statement or proof uses this declaration.
- dist_dist_dist_le_leftproof · cited by 3
- abs_norm_sub_norm_le_norm_inv_mulproof · cited by 3
- abs_norm_sub_norm_le_norm_neg_addproof · cited by 3
- abs_dist_sub_le_dist_add_addproof · cited by 1
- abs_dist_sub_le_dist_mul_mulproof · cited by 1
- KuratowskiEmbedding.embeddingOfSubset_dist_leproof · cited by 1
- Convexity.dist_convexCombPair_convexCombPairproof · cited by 1
- PseudoMetricSpace.dist_eq_of_dist_zeroproof · cited by 0