Theorems · Theorem · general topology
PiCountable.edist_eq_tsum
∀ {ι : Type u_2} [inst : Encodable ι] {F : ι → Type u_3} [inst_1 : (i : ι) → EDist (F i)] (x y : (i : ι) → F i),
edist x y = ∑' (i : ι), min (2⁻¹ ^ Encodable.encode i) (edist (x i) (y i))- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- ENNRealstatement · cited by 9,879
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- EDist.ediststatement · cited by 735
- Encodablestatement and proof · cited by 140
- Encodable.encodestatement · cited by 118
- EDiststatement and proof · cited by 91
- PiCountable.ediststatement · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- PiCountable.edist_le_twoproof · cited by 1