Theorems · Theorem · general topology
PiCountable.dist_le_dist_pi_of_dist_lt
∀ {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}, dist x y < 2⁻¹ ^ Encodable.encode i → dist (x i) (y i) ≤ dist x y- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EncodablePseudoMetricSpace
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Cites9
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 and proof · cited by 1,539
- not_leproof · cited by 328
- Encodablestatement and proof · cited by 140
- Encodable.encodestatement and proof · cited by 118
- min_le_iffproof · cited by 15
- PiCountable.diststatement · cited by 3
- PiCountable.min_dist_le_dist_piproof · cited by 1
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