Theorems · Theorem · general topology
edist_congr_left
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x y z : α}, edist x y = 0 → edist z x = edist z y- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement and proof · cited by 735
- PseudoEMetricSpace.edist_commproof · cited by 52
- edist_congr_rightproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- eVariationOn.eq_of_edist_zero_onproof · cited by 2
- edist_congrproof · cited by 0