Theorems · Theorem · general topology
PiCountable.min_dist_le_dist_pi
∀ {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) (i : ι), min (2⁻¹ ^ Encodable.encode i) (dist (x i) (y i)) ≤ dist x y- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EncodablePseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Encodablestatement and proof · cited by 140
- inv_powproof · cited by 140
- dist_nonnegproof · cited by 126
- Encodable.encodestatement and proof · cited by 118
- le_minproof · cited by 21
- Summable.le_tsumproof · cited by 6
- PiCountable.diststatement · cited by 3
- PiCountable.dist_summableproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- PiCountable.dist_le_dist_pi_of_dist_ltproof · cited by 0