Theorems · Theorem · general topology
dist_comm
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y : α), dist x y = dist y x- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 188 results in Mathlib
- Foundations
- Depth 3 from the axioms, rests on 6 definitions · uses no axioms
- Assumes
- PseudoMetricSpace
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- PseudoMetricSpace.dist_commproof · cited by 2
Cited by188
Results whose statement or proof uses this declaration.
- dist_nonnegproof · cited by 126
- Metric.uniformity_basis_distproof · cited by 25
- dist_eq_norm_vsub'proof · cited by 21
- Metric.mem_closure_iffproof · cited by 18
- dist_triangle_rightproof · cited by 16
- dist_zero_leftproof · cited by 15
- Real.closedBall_eq_Iccproof · cited by 13
- dist_self_add_leftproof · cited by 11
- Metric.mem_closedBall'proof · cited by 11
- dist_triangle_leftproof · cited by 11
- Real.ball_eq_Iooproof · cited by 11
- Metric.mem_ball'proof · cited by 10