Theorems · Theorem · general topology
PiCountable.dist_eq_tsum
∀ {ι : Type u_2} [inst : Encodable ι] {F : ι → Type u_3} [inst_1 : (i : ι) → PseudoMetricSpace (F i)]
(x y : (i : ι) → F i), dist x y = ∑' (i : ι), min (2⁻¹ ^ Encodable.encode i) (dist (x i) (y i))- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EncodablePseudoMetricSpace
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- SummationFilter.unconditionalstatement · cited by 2,068
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- tsumstatement · cited by 1,148
- Encodablestatement and proof · cited by 140
- Encodable.encodestatement · cited by 118
- PiCountable.diststatement · cited by 3
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